Question

select the correct answer.
a logarithmic function, h, is plotted on the graph.
what is the approximate rate of change of this function on the interval -2, 2?
a. -9/8
b. 5/7
c. 4
d. -7/2

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = h(x)\) on the interval \([a,b]\) is \(\frac{h(b)-h(a)}{b - a}\). Here, \(a=-2\) and \(b = 2\).

Step2: Find \(h(-2)\) and \(h(2)\) from the graph

From the graph, when \(x=-2\), \(h(-2)=0\); when \(x = 2\), \(h(2)=-3.5\).

Step3: Calculate the average rate of change

Substitute into the formula: \(\frac{h(2)-h(-2)}{2-(-2)}=\frac{-3.5 - 0}{2 + 2}=\frac{-3.5}{4}=-\frac{7}{8}\)

Answer:

A. \(-\frac{7}{8}\)