Precalculus Examples

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

Step 1

Choose the starting and ending values from the table.

$(1, 2), (1, \frac{1}{3})$

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.

$m = \frac{\frac{1}{3} - (2)}{1 - (1)}$

Step 6

Simplify.

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Step 6.1

Multiply $- 1$ by $1$ .

$\frac{\frac{1}{3} - (2)}{1 - 1}$

Step 6.2

Subtract $1$ from $1$ .

$\frac{\frac{1}{3} - (2)}{0}$

Step 6.3

The expression contains a division by $0$ . The expression is undefined.

Undefined