Answer
See the explanation
Work Step by Step
Case-End Behavior of the graph of a polynomial function
When the leading coefficient is odd and is positive - Graph falls to the left and rises to the right
When the leading coefficient is odd and is negative-Graph rises to the left and falls to the right
When the leading coefficient is even and is positive-Graph rises to the left and right
When the leading coefficient is even and is negative-Graph falls to the left and right
$f(x)=x^5-x$
According to the leading coefficient test, since the leading coefficient is positive and the degree is odd. The graph of $f(x)$ falls to the left and rises to the right. But that is not the case with the graph shown which rises to the left and falls to the right.
The $y$-intercept of the $f(x)$ is $x=0$, $f(0)=0$ and the $x$-intercept of $f(x)$ is where $f(x)=x^5-x=0$,
$f(x)=x(x^4-1)=0$,
$x=0$ or $x=1$.But that is not the case with the graph shown which has $x$-intercept of $(-2, 0)$ or $(2, 0)$
