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Find the average rate of change of $g(x) = x + 15$ between $x = -5$ and $x = -5 + h$ , where $h \neq 0$ . $\newline$ Simplify your answer. Your answer may be a number or an expression in terms of $h$ .

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Average rate of change I

Full solution

Q. Find the average rate of change of

g(x) = x + 15

between

x = -5

and

x = -5 + h

, where

h \neq 0

.

\newline

Simplify your answer. Your answer may be a number or an expression in terms of

h

.

Calculate $g(x)$ : Calculate $g(x)$ at the initial point $x = -5$ . $\newline$ $g(-5) = -5 + 15 = 10$
Calculate $g(x)$ : Calculate $g(x)$ at the point $x = -5 + h$ . $\newline$ $g(-5 + h) = (-5 + h) + 15 = h + 10$
Find change: Find the change in $g(x)$ over the change in $x$ .
Change in $g(x)$ = $g(-5 + h) - g(-5) = (h + 10) - 10 = h$
Change in $x$ = $(-5 + h) - (-5) = h$
Calculate average rate: Calculate the average rate of change. $\newline$ Average rate of change = $\frac{\text{Change in } g(x)}{\text{Change in } x}$ = $\frac{h}{h}$ = $1$

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