Answer
Since rates of change are decreasing, the graph of $f(x)$ is concave down.
Work Step by Step
Calculate the rate of change between the following points of length 2.$(x_1, x_2)= (-1,1)$ ,$(x_2, x_3)= (1,3)$ and $(x_3, x_4)= (3,5)$
$$
\begin{aligned}
& \frac{\Delta f(x)}{\Delta x}=\frac{f(1)-f(-1)}{1-(-1)}=\frac{\left(4-1^2\right)-\left(4-(-1)^2\right)}{2}=0 . \\
& \frac{\Delta f(x)}{\Delta x}=\frac{f(3)-f(1)}{3-1}=\frac{\left(4-3^2\right)-\left(4-1^2\right)}{2}=-4 . \\
& \frac{\Delta f(x)}{\Delta x}=\frac{f(5)-f(3)}{5-3}=\frac{\left(4-5^2\right)-\left(4-3^2\right)}{2}=-8 .
\end{aligned}
$$
Since rates of change are decreasing, the graph of $f(x)$ is concave down.
