Question

using the function graph shown below, calculate the average rate of change from x = -5 to x = -3.

Explanation:

Step1: Determine the function values at \(x = -5\) and \(x=-3\)

From the graph, when \(x=-5\), \(y = 0\); when \(x = -3\), \(y=3\).

Step2: Use the average rate of change formula

The average rate of change formula is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x_1=-5\), \(f(x_1)=0\), \(x_2=-3\), \(f(x_2) = 3\).
Substitute into the formula: \(\frac{3 - 0}{-3-(-5)}=\frac{3}{-3 + 5}\).

Step3: Simplify the expression

\(\frac{3}{2}=1.5\)

Answer:

\(1.5\)