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Find the average rate of change of $k(x) = x - 8$ between $x = -7$ and $x = -7 + h$ , 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

k(x) = x - 8

between

x = -7

and

x = -7 + h

, where

h \neq 0

.

\newline

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

h

.

Calculate $k(x)$ : Calculate $k(x)$ at $x = -7$ and $x = -7 + h$ . $\newline$ $k(-7) = -7 - 8 = -15$ $\newline$ $k(-7 + h) = (-7 + h) - 8 = h - 15$
Find average rate: Find the average rate of change of $k(x)$ from $x = -7$ to $x = -7 + h$ . $\newline$ Average rate of change = $\frac{k(-7 + h) - k(-7)}{h}$ $\newline$ = $\frac{(h - 15) - (-15)}{h}$ $\newline$ = $\frac{h - 15 + 15}{h}$ $\newline$ = $\frac{h}{h}$ $\newline$ = $1$

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