Question

the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on the interval ( -5 leq x leq 3 )?

Explanation:

Step1: Find f(-5) and f(3)

From the graph, when \( x = -5 \), the y - value (f(-5)) is -6. When \( x = 3 \), the y - value (f(3)) is 10.

Step2: Use the average rate of change formula

The formula for the average rate of change of a function \( y = f(x) \) on the interval \([a,b]\) is \( \frac{f(b)-f(a)}{b - a} \). Here, \( a=-5 \), \( b = 3 \), \( f(a)=f(-5)=-6 \), \( f(b)=f(3)=10 \).
So, the average rate of change is \( \frac{f(3)-f(-5)}{3-(-5)}=\frac{10 - (-6)}{3 + 5}=\frac{10 + 6}{8}=\frac{16}{8}=2 \).

Answer:

2