Precalculus Examples

$\begin{array}{c} x & 0 \\ 1 & 2 \\ 3 & 4 \\ g (x) & 1 \\ 3 & 9 \\ 27 & 81 \end{array}$

Step 1

Choose the starting and ending values from the table.

$(1, 2), (27, 81)$

Step 2

To find the average rate of change, find the slope.

Step 3

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 4

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 5

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{81 - (2)}{27 - (1)}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Multiply $- 1$ by $2$ .

$m = \frac{81 - 2}{27 - (1)}$

Step 6.1.2

Subtract $2$ from $81$ .

$m = \frac{79}{27 - (1)}$

Step 6.2

Simplify the denominator.

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Step 6.2.1

Multiply $- 1$ by $1$ .

$m = \frac{79}{27 - 1}$

Step 6.2.2

Subtract $1$ from $27$ .

$m = \frac{79}{26}$

Step 7