Stitz-Zeager_College_Algebra_e-book

If we dene an intermediate function m1 x f x to take

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Unformatted text preview: (−3, −2) is on the graph of m, by computing m(−3) = (−3) + 3 − 2 = 0 − 2 = −2 We now turn our attention to reflections. We know from Section 1.1 that to reflect a point (x, y ) across the x-axis, we replace y with −y . If (x, y ) is on the graph of f , then y = f (x), so replacing y with −y is the same as replacing f (x) with −f (x). Hence, the graph of y = −f (x) is the graph of f reflected across the x-axis. Similarly, the graph of y = f (−x) is the graph of f reflected across the y -axis. Returning to inputs and outputs, multiplying the output from a function by −1 reflects its graph across the x-axis, while multiplying the input to a function by −1 reflects the graph across the y -axis.4 Theorem 1.4. Reflections. Suppose f is a function. • To graph y = −f (x), reflect the graph of y = f (x) across the x-axis by multiplying the y -coordinates of the points on the graph of f by −1. • To graph y = f (−x), reflect the graph of y = f (x) across the y -axis by multiplying the x-coordinates of the points on the graph of f by −1. Applying Theroem 1.4 to the graph of y = f (x) given at the beginning of the section, we can gr...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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