Answer:
[tex]Rate = 1[/tex]
Step-by-step explanation:
Given
[tex]g(x) = x + 7[/tex]
Interval: (-2,4)
Required
Determine the average rate of change
This is calculated using:
[tex]Rate = \frac{g(b) - g(a)}{b-a}[/tex]
Where:
[tex](a,b) = (-2,4)[/tex]
So, we have:
[tex]Rate = \frac{g(4) - g(-2)}{4-(-2)}[/tex]
[tex]Rate = \frac{g(4) - g(-2)}{4+2}[/tex]
[tex]Rate = \frac{g(4) - g(-2)}{6}[/tex]
Calculate g(4) and g(-2)
[tex]g(4) = 4 + 7 = 11[/tex]
[tex]g(-2) = -2 + 7 = 5[/tex]
So:
[tex]Rate = \frac{11 - 5}{6}[/tex]
[tex]Rate = \frac{6}{6}[/tex]
[tex]Rate = 1[/tex]
Hence, the average rate of change is 1
