2.1 Graphing Absolute Value Functions.notebook, Lecture notes of Pre-Calculus

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2.1 Graphing Absolute Value Functions.notebook September 29, 2016 Pg 65 2.1 Graphing Absolute Value Functions Essential Question: How can you identify the features of the graph of an absolute value function? Graphing and Analyzing the Parent Absolute Value Function Absolute value, written as |x|, represents the distance between x and 0 on a number line. As a distance, absolute value is always positive. For every point on a number line, there is another point on the opposite side of 0 that is the same distance from 0. For example, both 5 and —5 are five units away from 0. Thus, | —5| = 5 and|5| = 5. 5 units 5 units <-—__+—__+—_+—_ —5 0 5 Soman cot ‘The absolute value function |x|, can be defined peceise as Ixl= { Eg: When xis nonnegative, =x x ‘the function simply returns the number. When x is negative, the function returns the opposite of x. ® Complete the input-output table for f(x). x x>0 -8 foy= izi= {* on Plot the points you found on the coordinate grid. Use the points to complete the graph of the function. = \Q, / _ Ix) Now, examine your graph of f(x) = |x| and complete the following statements about the function. f(x) = |x| is symmetric about the Yy ANS and therefore is a(n) é VE function. . Gsess) yall | The domain of f(x) = |x| is ‘The range of f(x) = [xis Lo ) 0)) fe