Question

given the function $f(x) = -5x - 2$, calculate the average rate of change from $f(-2)$ to $f(0)$.
a. 5
b. -2
c. -5
d. -7

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) from \( x = a \) to \( x = b \) is given by \( \frac{f(b) - f(a)}{b - a} \). Here, \( a=-2 \) and \( b = 0 \).

Step2: Calculate \( f(-2) \)

Substitute \( x=-2 \) into \( f(x)=-5x - 2 \):
\( f(-2)=-5(-2)-2=10 - 2 = 8 \)

Step3: Calculate \( f(0) \)

Substitute \( x = 0 \) into \( f(x)=-5x - 2 \):
\( f(0)=-5(0)-2=0 - 2=-2 \)

Step4: Calculate the average rate of change

Using the formula \( \frac{f(b)-f(a)}{b - a} \) with \( a=-2 \), \( b = 0 \), \( f(-2)=8 \) and \( f(0)=-2 \):
\( \frac{f(0)-f(-2)}{0-(-2)}=\frac{-2 - 8}{0 + 2}=\frac{-10}{2}=-5 \)

Answer:

C. -5