Answer
$-41$
Work Step by Step
We are given the functions:
$$\begin{align*}
f(x)&=5x^3-3x^2\\
g(x)&=-2x^2-5.
\end{align*}$$
In order to calculate $g(2)-f(2)$ using a graphing calculator, we perform the following steps:
$\textbf{Step 1}$: Form the difference
Use $\textit{Function}$ from the $\textit{Y-Vars}$ menu. Enter $y_1=-2x^2-5$ and $y_2=5x^3-3x^2$. Then enter the difference as $y_3=y_1-y_2$.
$\textbf{Step 2}$: Evaluate the difference
On the home screen enter $y_3(2)$ and press Enter. We get:
$$y_3(2)=-41$$
Therefore $g(2)-f(2)=-41$.
