Question

select the correct answer.

this table represents function (f).

\

$$\begin{array}{|c|c|c|c|c|c|c|c|} \\hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\\ \\hline f(x) & -4.5 & -2 & -0.5 & 0 & -0.5 & -2 & -4.5 \\\\ \\hline \\end{array}$$

if function (g) is a quadratic function that contains the points ((-3, 5)) and ((0, 14)), which statement is true over the interval (-3, 0)?

• the average rate of change of (f) is the same as the average rate of change of (g).
• the average rate of change of (f) is less than the average rate of change of (g).
• the average rate of change of (f) is more than the average rate of change of (g).
• the average rates of change of (f) and (g) cannot be determined from the given information.

Explanation:

Calculate the average rate of change of \(f\) over \([-3, 0]\)

$$
LATEXBLOCK0
$$

Calculate the average rate of change of \(g\) over \([-3, 0]\)

$$
LATEXBLOCK1
$$

Compare the average rates of change

$$
LATEXBLOCK2
$$

Answer:

• The average rate of change of \(f\) is the same as the average rate of change of \(g\).
• The average rate of change of \(f\) is less than the average rate of change of \(g\). (Correct answer)
• The average rate of change of \(f\) is more than the average rate of change of \(g\).
• The average rates of change of \(f\) and \(g\) cannot be determined from the given information.