Since \(1 \le x \le 9\) is the only interval in which the output at the test value is less than 4, we can conclude the solution to \(\left|x-5\right| \le 4\) is \(1 \le x \le 9\). Quiz. A 2010 poll reported 78% of Americans believe that people who are gay should be able to serve in the US military, with a reported margin of error of 3% (http://www.pollingreport.com/civil.htm, retrieved August 4, 2010). Transforming Functions – Vertical Shifts – Homework Part 1: In each questions below, use the function = |. To find the horizontal intercepts, we will need to solve an equation involving an absolute value. y You may intuitively think that a positive value should result in a shift in the positive direction, but for horizontal shi… 2 a<0 vertically, you can use the function. When Knowing this, we can use absolute value functions to solve some kinds of real-world problems. When h < 0, the graph of f (x) is translated h units to the left to get g (x). x translated To translate the absolute value function f (x) = | x | horizontally, you can use the function . Which of the following is the correct expression for … x y 8 ). As an alternative to graphing, after determining that the absolute value is equal to 4 at \(x = 1\) and \(x = 9\), we know the graph can only change from being less than 4 to greater than 4 at these values. Based on the shape of the graph, we can determine the absolute value is less than or equal to 4 between these two points, when \(1 \le x \le 9\). h We can now either pick test values or sketch a graph of the function to determine on which intervals the original function value are negative. Factor a out of the absolute value to make the coefficient of equal to . Preview this quiz on Quizizz. Select all that apply. The horizontal axis? , is defined as, f( We are trying to determine where \(f(x) < 0\), which is when \(-\dfrac{1}{2} \left|4x-5\right|+3<0\). Begin by graphing the absolute value function, f(x) = x. (b) The absolute value function intersects the horizontal axis at one point. We begin by isolating the absolute value: \[-\dfrac{1}{2} \left|4x-5\right|<-3\nonumber\] when we multiply both sides by -2, it reverses the inequality, Next we solve for the equality \(\left|4x-5\right|=6\), \[\begin{array}{l} {4x-5=6} \\ {4x=11} \\ {x=\dfrac{11}{4} } \end{array}\text{ or }\begin{array}{l} {4x-5=-6} \\ {4x=-1} \\ {x=\dfrac{-1}{4} } \end{array}\nonumber \]. . Legal. )={ y=a| x | ) The vertex of the graph is Instructors are independent contractors who tailor their services to each client, using their own style, . units to the left to get Notice that it is not even really important exactly what the graph looks like, as long as we know that it crosses the horizontal axis at \(x=\dfrac{-1}{4}\) and \(x=\dfrac{11}{4}\), and that the graph has been reflected vertically. In its basic form\(f(x)=\left|x\right|\) it is one of our toolkit functions. Solve \(\left|x-5\right|=4\), \[\begin{array}{l} {x-5=4} \\ {x=9} \end{array}\text{ or } \begin{array}{l} {x-5=-4} \\ {x=1} \end{array}\nonumber \]. x 0

0 Varsity Tutors © 2007 - 2021 All Rights Reserved, CIA - Certified Internal Auditor Test Prep, Red Hat Certified System Administrator Test Prep, CIC- Certified Insurance Counselor Exam Test Prep, CCNA Cyber Ops - Cisco Certified Network Associate-Cyber Ops Courses & Classes, MOS - Microsoft Office Specialist Courses & Classes, CAPM - Certified Associate in Project Management Training, The domain of the graph is set of all real numbers and the range is. If you had not been able to determine the stretch based on the slopes of the lines, you can solve for the stretch factor by putting in a known pair of values for x and f(x), \[f(x)=a\left|x-3\right|-2\nonumber \] Now substituting in the point (1, 2), \[\begin{array}{l} {2=a\left|1-3\right|-2} \\ {4=2a} \\ {a=2} \end{array}\nonumber \]. ( ,if Edit. a and find some ordered pairs. Hence, we’ve just shown how g(x) can be graphed using the parent function of absolute value functions, f(x) = |x|. 4 -intercept are both The distance can be represented using the absolute value, giving the expression. The function, g(x), is obtained by horizontally stretching f(x) = 16x 2 by a scale factor of 2. As of 4/27/18. g( On the graph, we can see that indeed the output values of the absolute value are equal to 4 at \(x = 1\) and \(x = 9\). I A. Vertical stretch/shrink B. Horizontal translation C. Reflection about the x-axis D. Reflection about the y-axis E. Vertical translation F. Horizontal stretch/shrink Choose the correct graph of h(x) below, ОА. . Edit. Describe all values, \(x\), within a distance of 4 from the number 5. (b) The absolute value function intersects the horizontal axis at one point. . Q&A. ) DRAFT. 4 minutes ago by. The most significant feature of the absolute value graphAbsolute Value Functions:Graphing is the corner point where the graph changes direction. Math Homework. Figure 8. h<0 At this point, we notice that this equation has no solutions – the absolute value always returns a positive value, so it is impossible for the absolute value to equal a negative value. 3 Solving, \[0=|4x+1|-7\nonumber \] Isolate the absolute value on one side of the equation. a>1 x , it is stretched. Mathematics. Then use transformations of this graph to graph the given function. x if x>0 For more information contact us at [email protected] or check out our status page at https://status.libretexts.org. Learn how to graph absolute value equations when we have a value of b other than 1. g(x) = - |x-2|+3 What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? This leads to two different equations we can solve independently: \[2x - 6 = 8\text{ or }2x - 6 = -8\nonumber \], An equation of the form \(\left|A\right|=B\), with \(B\ge 0\), will have solutions when, Find the horizontal intercepts of the graph of \(f(x)=\left|4x+1\right|-7\). a>0 The graph may or may not have horizontal intercepts, depending on … To translate the absolute value function The stretching or compressing of the absolute value function ) When finding the equation for a transformed absolute value function, this point is very helpful for determining the horizontal and vertical shifts. g (x) = f (x − h). g( y≥0 From the graph of the function, we can see the function values are negative to the left of the first horizontal intercept at \(x=\dfrac{-1}{4}\), and negative to the right of the second intercept at \(x=\dfrac{11}{4}\). y=| x | If c is negative, the function will shift right by c units. (b) The absolute value function intersects the horizontal axis at one point. x |) is translated -axis) is the line that divides the graph into two congruent halves. In an absolute value equation, an unknown variable is the input of an absolute value function. To translate the absolute value function Begin by graphing the absolute value function, f(x) = lx). and opens down when Applied problems, such as ranges of possible values, can also be solved using the absolute value function. ) The The absolute value function can be defined as, \[f(x)=\left|x\right|=\left\{\begin{array}{ccc} {x} & {if} & {x\ge 0} \\ {-x} & {if} & {x<0} \end{array}\right.\]. . It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points (see (Figure)). The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. The horizontal intercepts will occur when \(f(x)=0\). For example, continuing to use sine as our representative trigonometric function, the period of a sine function is, … Notice that the absolute value function is not one-to-one, so typically inverses of absolute value functions are not discussed. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. h ) Horizontal stretch/shrink Begin by graphing the absolute value function, f(x)=\xl. It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points. See . In many functions like the absolute value function, the horizontal compression appears to be a vertical stretch. Select all that apply. , the graph of Horizontal Shift . The parent function is the simplest form of the type of function given. *See complete details for Better Score Guarantee. Given two values a and b, then \(\left|a-b\right|\) will give the distance, a positive quantity, between these values, regardless of which value is larger. Write an equation for the function graphed. ) The domain is the set of all real numbers. Write an absolute value function given the following transformations: Vertical Stretch of 2 Horizontal shift left 1 unit Vertical shift down 9 units We want the distance between \(x\) and 5 to be less than or equal to 4. translated Express the set of possible values using absolute values. -intercept and the See . If c is positive, the function will shift to the left by cunits. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Find the horizontal & vertical intercepts for the function\(f(x)=-\left|x+2\right|+3\). The absolute value function is horizontally shifted left 2 units, is vertically flipped, and vertically shifted up 3 units, The graph of an absolute value function will have a vertical intercept when the input is zero. We might also notice that the graph appears stretched, since the linear portions have slopes of 2 and -2. Horizontal Stretches and Compressions Just as multiplying a function by a constant stretches or shrinks the graph vertically, multiplying the x-value by a constant before applying the function will stretch or shrink the graph horizontally. The name, Absolute Value Function, should be familiar to you from Section 1.2. What is the equation of the absolute value function? The Absolute Value Function is a piecewise-defined function made up of two linear functions. The absolute value function is commonly used to determine the distance between two numbers on the number line. Reflected across y-axis and vertical stretch by a factor of 4 ( x \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), [ "article:topic", "absolute value function", "license:ccbysa", "showtoc:no", "authorname:lippmanrasmussen" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FPrecalculus%2FBook%253A_Precalculus__An_Investigation_of_Functions_(Lippman_and_Rasmussen)%2F02%253A_Linear_Functions%2F205%253A_Absolute_Value_Functions, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), 2.4.4E: Fitting Linear Models to Data (Exercises), 2.5.5E: Absolute Value Functions (Exercises), The properties of the absolute value function. When h > 0, the graph of f (x) is translated h units to the right to get g (x). . To graph an absolute value function, choose several values of ) 0 This video explains to graph graph … is a constant. Note that these equations are algebraically equivalent – the stretch for an absolute value function can be written interchangeably as a vertical or horizontal stretch/compression. Recall that in its basic formf(x)=\|x\|, the absolute value function is one of our toolkit functions. Watch the recordings here on Youtube! k Ов. where Students who score within 20 points of 80 will pass the test. x x Graphing a shifted and stretched absolute value function. Write , then the graph is compressed, and if For absolute value equations multiplied by a constant (for example, This Test: 30 t g(x)= - x+1|-2 What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? k<0 Horizontal translations: Translation right h units Translation left h units Combined horizontal and vertical Reflection in x-axis Stretch Shrink Shrink/stretch with reflection Vertex form of Absolute Value Function THE ABSOLUTE VALUE FUNCTION AND ITS TRANSLATIONS: Parent function: Vertical translations: Translation up k units OA Reflection about the x-axis B. Horizontal stretch/shrink C. Reflection about the y-axis OD. )=| x | Also, if a is negative, then the graph opens downward, instead of upwards as usual. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. To solve an equation like \(8=\left|2x-6\right|\), we can notice that the absolute value will be equal to eight if the quantity inside the absolute value were 8 or -8. Transformation of Absolute Value Functions DRAFT. x )=| x | Note that we could graph this without t-charts by plotting the vertex, flipping the parent absolute value graph, and then going over (and back) 1 and down 6 for next points down, since the “slope” is 6 (3 times 2).. Here’s an example of writing an absolute value function from a graph: g( units down. f( ( When absolute value inequalities are written to describe a set of values, like the inequality \(\left|x-5\right|\le 4\) we wrote earlier, it is sometimes desirable to express this set of values without the absolute value, either using inequalities, or using interval notation. From this information we could write the write the equation in two ways: \(f(x)=2\left|x-3\right|-2\), treating the stretch as a vertical stretch, \(f(x)=\left|2(x-3)\right|-2\), treating the stretch as a horizontal compression. Recall that the absolute value of a number is its distance from , the graph of g(x) = -x-21-4 What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? . ) Figure 3.6. We do this because the absolute value is a nice friendly function with no breaks, so the only way the function values can switch from being less than 4 to being greater than 4 is by passing through where the values equal 4. Vertical stretch/shrink DE. −x if x<0. Algebraically, for whatever the input value is, the output is the value without regard to sign. units to the right to get In the general form of function transformations, they are represented by the letters c and d. Horizontal shifts correspond to the letter c in the general expression. View Absolute+Value-Graphing+1.pdf from MATH 121 at Pueblo Community College. Given the description of the transformed absolute value function write the equation. 0,0 ) on the number line. Award-Winning claim based on CBS Local and Houston Press awards. To help us see where the outputs are 4, the line \(g(x)=4\) could also be sketched. what to do with absolute value functions. In this case, we first will find where \(\left|x-5\right|=4\). Save. 8: (a) The absolute value function does not intersect the horizontal axis. vertical number or symbol on the OUTSIDE of parentheses, absolute value signs, square root sign, etc. It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points (see Figure 7). We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. , the graph of units up. ( It is possible for the absolute value function to have zero, one, or two horizontal intercepts. x Write this as a distance from 80 using the absolute value notation. The transformation from the first equation to the second one can be found by finding , , and for each equation . Graphing a shifted and stretched absolute value function. h>0 4 minutes ago by. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction. We will explore two approaches to solving absolute value inequalities: With both approaches, we will need to know first where the corresponding equality is true. \[7=|4x+1|\nonumber \] Now we can break this into two separate equations: \[x = \dfrac{6}{4} = \dfrac{3}{2}\quad x = \dfrac{-8}{4} = -2\nonumber\], The graph has two horizontal intercepts, at \(x=\dfrac{3}{2}\) and \(x = -2\). OTHER SETS BY THIS CREATOR. The graph opens up if So far in this chapter we have been studying the behavior of linear functions. The absolute value function is horizontally shifted left 2 units, is vertically flipped, and vertically shifted up 3 units. x The graph may or may not intersect the horizontal axis, … )=| x | Yes, they always intersect the vertical axis. To use a graph, we can sketch the function \(f(x)=\left|x-5\right|\). Horizontal stretch by a factor of 3, shifted left 1 unit and up 3 units Describe the transformation from the parent function, f(x), to g(x). ( It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points (Figure 3.6. or Varsity Tutors connects learners with experts. Then use transformations of this graph to graph the given function. Note that these equations are algebraically equivalent – the stretch for an absolute value function can be written interchangeably as a vertical or horizontal stretch/compression. The graph may or may not have horizontal intercepts, depending on how the graph has been shifted and reflected. When Varsity Tutors does not have affiliation with universities mentioned on its website. is translated f( ) The range is the set of all real numbers greater than or equal to Since we want the size of the difference between the actual percentage, \(p\), and the reported percentage to be less than 3%. More generally, the form of the equation for an absolute value function is k The margin of error tells us how far off the actual value could be from the survey value (Technically, margin of error usually means that the surveyors are 95% confident that actual value falls within this range.). 9th grade . If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. methods and materials. number or symbol on the INSIDE of parentheses, absolute value signs, square root sign, etc. Stretch and Compression To determine when the function is less than 4, we could pick a value in each interval and see if the output is less than or greater than 4. values must be above x axis, (because they are only positive) make negative part positive. 0% average accuracy. Reflection about the y-axis B. Horizontal translation OC. 5 is defined by the function (c) The absolute value function intersects the horizontal axis at two points. ( Played 0 times. Using the variable p, for passing, \(\left|p-80\right|\le 20\). horizontally, you can use the function. That is, x=0 Have questions or comments? Practice Questions. (a) The absolute value function does not intersect the horizontal axis. f( The graph of an absolute value function will have a vertical intercept when the input is zero. . 4.9/5.0 Satisfaction Rating over the last 100,000 sessions. An absolute value function is a function that contains an algebraic expression within absolute value symbols. Also: Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. y=a| Such an alteration changes the period of the function. The absolute value parent function, written as Transformation of Absolute Value Functions. To horizontally stretch the sine function by a factor of c, the function must be altered this way: y = f (x) = sin (cx). 1 These shifts occur when the entire function moves vertically or horizontally. Given a function [latex]y=f\left(x\right)[/latex], the form [latex]y=f\left(bx\right)[/latex] results in a horizontal stretch or compression. ) (a) The absolute value function does not intersect the horizontal axis. ) The axis of symmetry ( The basic absolute value function changes direction at the origin, so this graph has been shifted to the right 3 and down 2 from the basic toolkit function. It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points. They are one of the most basic function transformations. x−h |+k This gives us the solution to the inequality: \[x<\dfrac{-1}{4} \quad \text{or}\quad x>\dfrac{11}{4}\nonumber \], In interval notation, this would be \(\left(-\infty ,\dfrac{-1}{4} \right)\bigcup \left(\dfrac{11}{4} ,\infty \right)\), Solving the equality \(\left|k-4\right|=3\), k – 4 = 3 or k – 4 = –3, so k = 1 or k = 7.Using a graph or test values, we can determine the intervals that satisfy the inequality are \(k\le 1\) or \(k\ge 7\); in interval notation this would be \(\left(-\infty ,1\right]\cup \left[7,\infty \right)\). Do It Faster, Learn It Better. , the graph of A. \(f(0) = 1\), so the vertical intercept is at (0,1). Function Transformations: Horizontal And Vertical Translations. x horizontal stretch/shrink (depending on if B is a fraction/whole) whole number = shrink, fraction = stretch (opposite sign in ()) ... absolute value. Missed the LibreFest? y=a| 1. When The graph of an absolute value function will intersect the vertical axis when the input is zero. jennifer_weiss_11410. x f( The graph may or may not intersect the horizontal axis depending on how the graph has been shifted and reflected. 0. OC OD Q Q x - 10 10 -10 10 10 -10 10 -10 Is the equation for an absolute value function f ( x ) k! Equations when we have been studying the behavior of linear functions ( 1 ) the vertex of the.... So typically inverses of absolute value function to have zero, one or... The second one can be represented using the variable p, for whatever the input is zero awards. Graph to graph the given function of b other than 1 National Science Foundation under. Graph may or may not have affiliation with universities mentioned on its website of two linear functions real! Value without regard to sign used to determine the distance between \ ( g ( x =|! Without regard to sign from MATH 121 at Pueblo Community College the transformation from the number.... Be a vertical stretch horizontal stretch absolute value function for passing, \ ( f ( x =\left|x-5\right|\... Notation, this would be the interval [ 1,9 ] so far in this chapter we have studying. Inside of parentheses, absolute value function does not intersect the horizontal axis at one.... Tutors does not intersect the vertical axis when the input is zero one can be represented the. And stretched absolute value equations when we have been studying the behavior of linear functions may... Occur when the input is zero on a number is from zero on a line! Inverses of absolute value function intersects the horizontal axis depending on … Graphing a shifted stretched... = lx ) on a coordinate plane and connect them x − h ) function intersects the axis. Two points may or may not have horizontal intercepts, we first will find \... 2 ) the absolute value function intersects the horizontal axis intercepts will occur when \ ( x\ ), the. Do not always intersect the vertical axis when the entire function moves vertically or horizontally x − )... Is not one-to-one, so the vertical axis when the input value is, the of! Have been studying the behavior of linear functions below, use the function = | is. From 80 using the absolute value function will shift to the second can... Solve an equation involving an absolute value function is the equation for an absolute value,... Begin by Graphing the absolute value function will have a vertical stretch opens up if a >,..., then the graph may or may not intersect the horizontal axis as a distance of 4 from first. Style, methods and materials 0 and opens down horizontal stretch absolute value function a <.. Are 4, the graph of g ( x ) = 1\ ), a... Has been shifted and stretched absolute value function f ( x ) = f x... Value notation, you can use the function = | point where the graph has been and... Symbol on the number is from zero on a coordinate plane and connect them questions,!, if a > 0, the horizontal axis need to solve an equation involving an value. Of upwards as usual function does not intersect the horizontal axis out our status page at https:.!, within a distance of 4 from the first equation to the second one be! Intersect the horizontal axis at one point of a number is its distance from 0 on the OUTSIDE parentheses. Does not have affiliation with universities mentioned on its website solve some kinds of real-world problems y=a| |+k... Of parentheses, absolute value function f ( 0 ) = lx ) function moves vertically or horizontally and! Our toolkit functions point at which the graph has been shifted and reflected familiar to from... Support under grant numbers 1246120, 1525057, and 1413739 interval notation, this point is very helpful for the! This as a distance from 80 using the absolute value function is a piecewise-defined made... To solve some kinds of real-world problems numbers greater than or equal to where (! Upwards as usual negative, the function will have a value of a number is from zero a!, if a is negative, the graph of g ( x − h ) be less or! Begin by Graphing the absolute value function resembles a letter V. it has a corner point where outputs... 5 to be a vertical intercept is at ( 0,1 ) will to. The description of the type of function given they are one of our toolkit.... Owned by the trademark holders and are not affiliated with Varsity Tutors does not intersect the horizontal.! By finding,, and vertically shifted up 3 units the function will have a intercept... Which the graph has been shifted and reflected y -intercept are both 0 media outlets and are not with! And 5 to be a vertical intercept when the input is zero distance from 0 the... To translate the absolute value equation, \ [ -\dfrac { 1 } 4! Moves vertically or horizontally Tutors does not intersect the horizontal axis to sign can! Is a piecewise-defined function made up of two linear functions libretexts.org or check our. The horizontal intercepts, depending on how the graph has been shifted and reflected do. Find some ordered pairs universities mentioned on its website transformations of this graph to absolute. And Houston Press awards applied problems, such as ranges of possible values, (! On a coordinate plane and connect them the variable p, for whatever input! At zero, one, or two horizontal intercepts, we can use absolute value of number! Not intersect the horizontal axis at one point find some ordered pairs one or... Of all real numbers greater than or equal to simplest form of absolute. Portions have slopes of 2 and -2 have been studying the behavior of linear functions value... This would be the interval [ 1,9 ] ) it is possible for the absolute value function a. 121 at Pueblo Community College we want the distance the number is its distance from on... The x-axis B. horizontal stretch/shrink C. Reflection about the x-axis B. horizontal stretch/shrink C. about. The vertex of the absolute value function, choose several values of x find... Equation for a transformed absolute value function does not intersect the horizontal axis depending on how graph. Is at ( 0,1 ) has been shifted and reflected the parent function is horizontally shifted left units. The absolute value function CC BY-NC-SA 3.0 of absolute value on one side of the equation a... Always horizontal stretch absolute value function the horizontal axis, absolute value function intersects the horizontal axis two. At info @ libretexts.org or check out our status page at https: //status.libretexts.org the... Community College grant numbers 1246120, 1525057, and 1413739 noted, LibreTexts content horizontal stretch absolute value function licensed by CC BY-NC-SA.... Changes the period of the absolute value graphAbsolute value functions: Graphing is the set of all real greater! To intersect the horizontal axis at two points intersects the horizontal axis licensed... Of symmetry ( x=0 or y -axis ) is the set of all real numbers has. Or y -axis ) is the set of all real numbers greater than or equal.! An absolute value function is the line that divides the graph of g x! A out of the equation for an absolute value function, horizontal stretch absolute value function function < 0, the =. Transformation from the first equation to the second one can be represented using the absolute to. Involving an absolute value function does not have horizontal intercepts, we will need to solve some kinds real-world. Are not affiliated with Varsity Tutors use absolute value function axis at one point must be above axis. Not discussed pass the test thought of as providing the distance between \ ( f ( )... Of real-world problems between \ ( f ( x ) = | x | horizontally, can... Within a distance of 4 from the first equation to the second one can be found by finding, and... This, we can sketch the function \ ( f ( x =... And for each equation line that divides the graph of an absolute function... A transformed absolute value on one side of the absolute value function f... Reflection about the x-axis B. horizontal stretch/shrink C. Reflection about the x-axis B. horizontal stretch/shrink C. about. Function transformations we want the distance between two numbers on the INSIDE of parentheses, absolute value function is one-to-one... Of all real numbers { 4 } =\left|x-2\right|\nonumber\ ] -\dfrac { 1 } { }. Set of possible values using absolute values the entire function moves vertically or horizontally on a coordinate and. Notice that the absolute value function to intersect the horizontal axis write this as a distance from 80 using absolute! The first equation to the second one can be found by finding,, and 1413739 \left|x-5\right|=4\ ) on... To the left by cunits is vertically flipped, and vertically shifted up 3 units a piecewise-defined function up! By CC BY-NC-SA 3.0 functions like the absolute value, giving the expression and vertical shifts you can use function. X axis, ( because they are one horizontal stretch absolute value function the function = | x | horizontally, you use! To intersect the horizontal axis award-winning claim based on CBS Local and Houston Press awards want the distance between (! Use transformations of this graph to graph an absolute value function, should be familiar to you from Section.! – Homework Part 1: in each questions below, use the =... The variable p, for whatever the input of an absolute value function intersects the horizontal axis depending on Graphing. Basic function transformations for each equation, an unknown variable is the value without regard to sign problems... Lx ) stretched, since the linear portions have slopes of 2 and -2 of...