Introduction to absolute value functions college algebra. Solving absolute value equations graphing absolute value functions solving absolute value inequalities if youre seeing this message, it means were having trouble loading external resources on our website. Solving absolute value equations kuta software llc. Eighth grade lesson graphing absolute value functions day. The graph of f xx is vshaped and symmetric about the yaxis.
Oct 09, 2017 this algebra video tutorial provides a basic introduction into graphing absolute value functions. The remaining properties are proved similarly and are left for the exercises. When solving equations with absolute value we can end up with more than one possible answer. Taking the absolute value of a negative number makes it positive. The graphs of all other absolute value functions are transformations of the graph of the parent function fx. An axis of symmetry of the graph of a function is a. The absolute value function is commonly thought of as providing the distance the number is from zero on a.
Absolute value equations worksheet 2 pdf view answers. Identify what the isolated absolute value is set equal to a. Algebra 34 unit 1 absolute value functions and equations. In order to accomplish this, we will spend at least 15 minutes making predictions about the appearance of absolute value functions and then evaluating our predictions using a graphing calculator.
The absolute value function, and its properties tamu math. To really get it, students need to see absolute value a. Students graph each piecewise function the functions are given on a slip of paper, iden. For this reason, graphs of absolute value functions tend not to look quite like the graphs of linear functions that youve already studied. Because of this, absolutevalue functions have graphs which make sharp turns where the graph would otherwise have crossed the xaxis. This is because what is in the absolute value can be either negative or positive and we must account for both possibilities when solving equations. Transformations of the absolute value parent function absolute value transformations of other parent functions absolute value transformations can be tricky, since we have two different types of problems. Use the questions to elicit student groups to share their responses.
A a quadratic function looks like a u that opens up or sometimes down. In this section, we will investigate absolute value functions. This is the graph of the absolute value of a linear function. Horizontal shift h units h is special always do the opposite of what you see vertical shift k units vertex is h, k a is like the slope for absolute value graphs. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. Solving absolute value equations graphing absolute value functions solving absolute value inequalities our mission is to provide a free, worldclass education to anyone, anywhere. Then hand each group 2 worksheets and a bag of absolute value transformation matchingmania cards. Absolute value functions in order to graph an absolute value function, you will be using many of the same methods you did for quadratics.
In this chapter, you will learn about absolute value and reciprocal functions. The absolute value function, and its properties one of the most used functions in mathematics is the absolute value function. Eighth grade lesson graphing absolute value functions day 1. Identify the vertex, axis of symmetry, x and yintercepts, domain, and range. You may have been taught that jxjis the distance from the real number xto the 0 on the number. For parent functions and general transformations, see the parent graphs and transformations section. How to find the domain and range from an absolute value. Absolute value and reciprocal functions practice exam 1. Understanding the shape to begin with it is very helpful to understand the shape of your function. The most significant feature of the absolute value graphabsolute value functions.
Dec 23, 2019 knowing how to solve problems involving absolute value functions is useful. The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. Finally well conclude our work in this chapter by developing. So, whether youre teaching absolute value before another topic, or introducing it for the first time, here are 11 absolute value activities that will help student understand and remember absolute value. Use the definition of the absolute value function to show that f x i x is an even function. Graphing quadratic, absolute value, and cubic functions 1. Recall that in its basic form latex\displaystylef\leftx\rightxlatex, the absolute value function, is one of our toolkit functions. At the end of the explain phase, students should be able to communicate. A step function is discontinuous cannot draw a step function without removing your pencil from your paper. Piecewise functions puzzle linear, absolute value, and quadratic functions this cutout puzzle was created to help students practice graphing a piecewise function along with identifying its domain and range. Use symmetry to plot a third point and then complete the graph. These piecewise definitions will help us draw the graphs of a variety of absolute value functions. To graph an absolute value function, choose several values of x and find some ordered pairs. Purplemath explains how these graphs work, and how to get full credit when doing this sort of graphing.
Its definition and some of its properties are given below. In all three activities, the graphs are posted around the room. Step functions a step function or staircase function is a piecewise function containing all constant pieces. When finding the equation for a transformed absolute value function, this point is very helpful for determining the horizontal and vertical shifts. Graph each absolutevalue function on a separate sheet of paper. Integers, opposites, absolute value opposites and absolute values. The parent function y 0x 0 is translated 2 units to the right, vertically stretched by the factor 3, and translated 4 units up. Transformations of absolute value functions performing absolute.
To do this we will need to sketch the graph of the equation and then determine how low and how high the graph travels for. They are the same distance from 0 on the number line, but in opposite directions. Problem solving use acquired knowledge to solve practice problems with absolute value functions additional learning. The vertex is the point where the graph changes direction. You will split each absolute value equation into two separate equations, then solve them to find your two solutions. Explore 1 graphing and analyzing the parent absolute value function integrate technology using calculators to graph the parent absolute value function can illustrate that other absolute value.
The first activity is a true scavenger hunt in that the student is give a clue abo. Intro to absolute value equations and graphs video khan academy. Key concept general form of the absolute value function problem 1 analyzing the graph of f x. Function absolute value, linear, quadratic worksheets. The real absolute value function is continuous everywhere. Absolute value function an absolute value function is a function that contains an absolute value expression. I can graph an absolute value function by performing. Typesfunctionexploration linear and quadratic from i drive. However, because of how absolute values behave, it is important to include negative inputs in your tchart when graphing absolutevalue functions. Since a real number and its opposite have the same absolute value, it is an even function, and is hence not invertible. You may have been taught that jxjis the distance from the real number xto 0 on the number line.
Absolute value functions 365 explain the explain portion of the lesson is directed by the teacher to allow the students to formalize their understanding of the teks addressed in the lesson. The absolute value function, denoted as or, is defined as the function that sends a real number to itself if it is nonnegative and to its negative if it is negative. How could i work on these functions with two or more absolute values. How to graph absolute value functions, basic introduction. Knowing how to solve problems involving absolute value functions is useful. For example, we may need to identify numbers or points on a line that are at a specified distance from a given reference point. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.
Absolute value function the absolute value of a real number x, jxj, is jxj. The vertical stretch or compression factor is 0a 0, the vertex is located at h, k, and the axis of symmetry is the line x h. Problem 6 problem 5 continued to find the yintercept, set x 0. You will also learn how they are used to solve problems. The real absolute value function is a piecewise linear. Every absolute value function has either a maximal point or a minimal point which is known as the vertex. One of the most used functions in mathematics is the absolute value function. I think it is important for students to make a visual connection to absolute value functions before introducing the general formula. Absolute value equations worksheet 3 here is a 9 problem worksheet where you will have the chance to solve some absolute value equations all by yourself.
O q pmla bdmef gwfi6tvh t kidn uf7i wn5imtfe f ba0l eg0e kb. The absolute value of a number is the number of units it is from 0 on the. To understand how the absolute value can be applied to the real world, well look at two topics. Learn how to think about absolute value as distance from zero, and practice finding absolute values. Graphing is the corner point where the graph changes direction. The highest or lowest point on the graph of an absolute value function is called the vertex. Absolute value functions maximizing algebra ii performance student lesson. Translating graphs of absolute value functions absolute value function, p. This is a set of 12 graphs of absolute value functions and 3 different activities to go along with them. Learn how to identify the domain and range of functions from equations.
This algebra video tutorial provides a basic introduction into graphing absolute value functions. So, for example, j5j 5 and j 5j 5, since each is 5 units from 0 on the number line. Absolute value functions 359 engage the engage portion of the lesson is designed to provide students with a concrete connection to. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. What is considered normal with regard to the temperature of the human body and. An absolute value equation is an equation in which the unknown variable appears in absolute value bars. Absolute value and reciprocal functions key terms absolute value absolute value function piecewise function invariant point absolute value equation reciprocal function asymptote. Graphing quadratic, absolute value, and cubic functions. Typesfunctionexploration cubic and absolute value from i drive. In your own words, write the meaning of each vocabulary term. Algebra 2 absolute value functions and transformations.