Question

what is the average rate of change of the function from x = 1 to x = 3?
options: 10, 12.5, 15, 30

Explanation:

Step1: Find y-values at x=1 and x=3

From the graph, at \( x = 1 \), \( y = 10 \); at \( x = 3 \), \( y = 40 \).

Step2: Apply average rate of change formula

The formula for average rate of change is \( \frac{f(b)-f(a)}{b - a} \), where \( a = 1 \), \( b = 3 \), \( f(a)=10 \), \( f(b)=40 \).
Substitute values: \( \frac{40 - 10}{3 - 1}=\frac{30}{2}=15 \).

Answer:

15