Question

f(x) = x^2 - 2; -2, -1
use the given function or the graph to find the average rate of change.
ans.

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is given by \(\frac{f(b) - f(a)}{b - a}\). Here, \( a=-2 \), \( b = - 1 \), and \( f(x)=x^{2}-2 \).

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

Substitute \( x=-2 \) into \( f(x) \):
\( f(-2)=(-2)^{2}-2=4 - 2=2 \)

Step3: Calculate \( f(-1) \)

Substitute \( x = - 1 \) into \( f(x) \):
\( f(-1)=(-1)^{2}-2=1 - 2=-1 \)

Step4: Apply the average rate of change formula

Using the formula \(\frac{f(b)-f(a)}{b - a}\) with \( a=-2 \), \( b=-1 \), \( f(-2) = 2 \), and \( f(-1)=-1 \):
\(\frac{f(-1)-f(-2)}{-1-(-2)}=\frac{-1 - 2}{-1 + 2}=\frac{-3}{1}=-3\)

Answer:

\(-3\)