Answer
The function can’t be represented by the provided graph since the end behavior comes out to be different than that shown and the intercepts are different as well.
Work Step by Step
First check the sign of the leading coefficient for checking the end behavior. Since the leading coefficient in the given function is positive, it should first rise and then fall. But in the given graph, we observe that it first falls and then rises. Due to this contradiction, it can be concluded that the graph does not represent the function $f\left( x \right)={{x}^{5}}-x$.
Now, factorize the given function $f\left( x \right)={{x}^{5}}-x$ as,
$\begin{align}
& f\left( x \right)={{x}^{5}}-x \\
& =x\left( {{x}^{4}}-1 \right) \\
& =x\left( {{x}^{2}}-1 \right)\left( {{x}^{2}}+1 \right) \\
& =x\left( x-1 \right)\left( x+1 \right)\left( {{x}^{2}}+1 \right)
\end{align}$
Then, put $f\left( x \right)=0$ to get the x-intercepts as $x=0,\pm 1,\pm \ i.$
However, the graph shows that the x-intercepts are $0,\pm 2$.
So, this also indicates that the given graph can’t represent the function $f\left( x \right)={{x}^{5}}-x.$
