Question

the function $y = f(x)$ is graphed below. plot a line segment connecting the points on $f$ where $x = 1$ and $x = 2$. use the line segment to determine the average rate of change of the function $f(x)$ on the interval $1 \leq x \leq 2$. plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Find f(1) and f(2) from the graph

From the graph, when \( x = 1 \), the \( y \)-value ( \( f(1) \)) is -10 (assuming the grid and the curve's position). When \( x = 2 \), the \( y \)-value ( \( f(2) \)) is 20 (from the graph's grid and the curve's point at \( x = 2 \)).

Step2: Apply the average rate of change formula

The formula for the average rate of change of a function \( f(x) \) on the interval \([a, b]\) is \( \frac{f(b)-f(a)}{b - a} \). Here, \( a = 1 \), \( b = 2 \), \( f(a)=f(1)=- 10 \), \( f(b)=f(2)=20 \).

Substitute the values into the formula:
\[
\frac{f(2)-f(1)}{2 - 1}=\frac{20-(-10)}{2 - 1}=\frac{20 + 10}{1}=\frac{30}{1}=30
\]

Answer:

The average rate of change of \( f(x) \) on the interval \( 1\leq x\leq2 \) is \( 30 \).