Precalculus (6th Edition) Blitzer

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

Chapter 2 - Cumulative Review Exercises - Page 435: 15

Answer

The graph is shown below:

Work Step by Step

To find the x-intercepts of the function equate the function ${{x}^{2}}\left( x-3 \right)$ to zero. $\begin{align} & {{x}^{2}}\left( x-3 \right)=0 \\ & x=0,3 \end{align}$ Thus, $x=0$ and $x=3$ are the x-intercepts of the function. To find the y-intercept of the function, find the value of $f\left( 0 \right)$. $\begin{align} & f\left( 0 \right)={{0}^{2}}\left( 0-3 \right) \\ & =0 \end{align}$ Thus, the y-intercept is 0. Substitute x with $-x$ to check the symmetry of the function: $\begin{align} & f\left( -x \right)={{\left( -x \right)}^{2}}\left( -x-3 \right) \\ & =-{{x}^{2}}\left( x+3 \right) \end{align}$ Since $f\left( x \right)\ne f\left( -x \right)$, the graph is not symmetric with respect to the y-axis and since $f\left( -x \right)\ne -f\left( x \right)$, thus, the graph is not symmetric through the origin.
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