Question

A function labeled f left-parenthesis x right-parenthesis is graphed on the coordinate plane.A function labeled f left-parenthesis x right-parenthesis is graphed on the coordinate plane. The graph is decreasing from x equals negative infinity to approximately x equals negative 2.3, then increases until approximately x equals negative 0.5. The graph decreases to point P left-parenthesis 1 comma 0 right parenthesis and then increases, passing through point Q left parenthesis 2 comma 3 right parenthesis.
Question
Use the graph to answer the question.
What is the average rate of change of f left parenthesis x right parenthesis between P and Q?
(1 point)
Responses

one third
Image with alt text: one third

1
1

start fraction 3 over 2 end fraction
Image with alt text: start fraction 3 over 2 end fraction

3

Answer 1

To calculate the average rate of change of the function \( f(x) \) between points \( P(1, 0) \) and \( Q(2, 3) \), we use the formula for the average rate of change over an interval \([a, b]\):

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

In this case:

- \( a = 1 \) and \( f(1) = 0 \) (the point P)
- \( b = 2 \) and \( f(2) = 3 \) (the point Q)

Plugging these values into the formula, we get:

\[
\text{Average Rate of Change} = \frac{f(2) - f(1)}{2 - 1} = \frac{3 - 0}{2 - 1} = \frac{3}{1} = 3
\]

So, the average rate of change of \( f(x) \) between points \( P \) and \( Q \) is \( 3 \).

The correct response is:

3