Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.6 - Transformations of Functions - Exercise Set - Page 243: 132

Answer

To reflect the graph of the function about the y-axis, the $x$ values of the function are replaced with $-x$ in the function’s equation $f\left( x \right)$.

Work Step by Step

Consider the function $f$, having equation $y=f\left( x \right)$. In a function, if we substitute x by –x, the values of the function obtained at x will now be obtained at –x and the corresponding values of y will remain the same. The graph of the function that is reflected about the y-axis be $g$. Then, for the reflection about the y-axis, the y-coordinate of the reflected graph, $g$ , will remain the same as that of $f$ but the x-coordinates of $g$ will have exactly opposite values as the x-coordinates of $f$ , that is, $\begin{align} & x'=-x \\ & y'=y \\ \end{align}$ Thus, the x value of the function is to be replaced by –x for a reflection about the y-axis, that is, $g\left( x \right)=f\left( -x \right)$ Hence, the points on the reflected graph about the y-axis will have points of the form $\left( -x,f\left( -x \right) \right)$.
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