Answer:
Part A:
The correct option is C.
The graph represents the function:
[tex]\begin{cases}-\frac{1}{2}x,x\le0 \\ x,x>0\end{cases}[/tex]
Part B:
The average rate of change is 1
Explanation:
Part A:
The graph is represents the function:
[tex]\begin{cases}-\frac{1}{2}x,x\le0 \\ x,x>0\end{cases}[/tex]
Part B:
The average rate of change on the interval -3 < x < -1 is
[tex]\begin{gathered} \frac{f(-1)-f(-3)}{-3-(-1)} \\ \\ =\frac{-\frac{1}{2}(-1)-\lbrack-\frac{1}{2}(-3)\rbrack}{-3+1} \\ \\ =\frac{-\frac{1}{2}-\frac{3}{2}}{-2} \\ \\ =\frac{-2}{-2}=1 \end{gathered}[/tex]
