## Precalculus (10th Edition)

1) The $x$-intercept is $(3,0)$, and the $y$-intercept is $(0,-27)$. 2) The graph of the equation $y={{x}^{3}}-27$ is not symmetric with respect to the $x$-axis, $y$-axis, and the origin.
To find $x$-intercept(s), let$y=0$ $\Rightarrow \,\,0={{x}^{3}}-27$ $\Rightarrow \,\,{{x}^{3}}=\,27$ $\Rightarrow \,\,x\,=\,3$ Therefore, the $x$-intercept is $(3,0)$ To find $y$-intercept(s), let $x=0$ $\Rightarrow \,\,y=0-27$ $\Rightarrow \,\,y=-27$ The $y$-intercept is $(0,-27)$ To test for symmetry with respect to the $x$-axis, replace $y$ with $-y$. If the result is equivalent to the original equation, then the equation is symmetric with respect to the $x$-axis. $\Rightarrow (-y)={{x}^{3}}-27$ is not equivalent to the equation $y={{x}^{3}}-27$. Hence, the graph of the equation $y={{x}^{3}}-27$ is not symmetric with respect to the $x$-axis To test for symmetry with respect to the $y$-axis, replace $x$ with$-x$. If the result is equivalent to the original equation, then the equation is symmetric with respect to the $y$-axis. $\Rightarrow y={{(-x)}^{3}}-27$ is not equivalent to the equation $y={{x}^{3}}-27$. Hence, the graph of the equation $y={{x}^{3}}-27$ is not symmetric with respect to the $y$-axis. To test for symmetry with respect to the origin, replace $x$ wutg $x$ and $y$ with $-y$. If the result is equivalent to the original equation, then the equation is symmetric with respect to the origin. $\Rightarrow \,-y={{(-x)}^{3}}-27$ is not equivalent to the equation $y={{x}^{3}}-27$ Hence, the graph of the equation $y={{x}^{3}}-27$ is not symmetric with respect to the origin.