What is the average rate of change of f(x)𝑓(𝑥) from x1=−2𝑥1=−2 to x2=3𝑥2=3? Please write your answer as an integer or simplified fraction.f(x)=−4x+3

1. Break Down the Problem

We need to find the average rate of change of the function $f(x) = -4x + 3$ between the points $x_1 = -2$ and $x_2 = 3$.

2. Relevant Concepts

The average rate of change of the function $f(x)$ from $x_1$ to $x_2$ is given by the formula:

$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

3. Analysis and Detail

1. Calculate $f(x_1)$ and $f(x_2)$:

   • $f(-2) = -4(-2) + 3 = 8 + 3 = 11$
   • $f(3) = -4(3) + 3 = -12 + 3 = -9$

2. Apply the average rate of change formula: $\text{Average Rate of Change} = \frac{f(3) - f(-2)}{3 - (-2)} = \frac{-9 - 11}{3 + 2} = \frac{-20}{5} = -4$

4. Verify and Summarize

The average rate of change is confirmed by the calculations, and the values were substituted correctly.

Final Answer

The average rate of change of $f(x)$ from $x_1 = -2$ to $x_2 = 3$ is $-4$.