Precalculus Examples

$y = 2 x - 2$ , $[- 2, 7]$

Step 1

Substitute using the average rate of change formula.

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Step 1.1

The average rate of change of a function can be found by calculating the change in $y$ values of the two points divided by the change in $x$ values of the two points.

$\frac{f (7) - f (- 2)}{(7) - (- 2)}$

Step 1.2

Substitute the equation $y = 2 x - 2$ for $f (7)$ and $f (- 2)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(2 (7) - 2) - (2 (- 2) - 2)}{(7) - (- 2)}$

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $2$ by $7$ .

$\frac{14 - 2 - (2 (- 2) - 2)}{7 - (- 2)}$

Step 2.1.2

Multiply $2$ by $- 2$ .

$\frac{14 - 2 - (- 4 - 2)}{7 - (- 2)}$

Step 2.1.3

Subtract $2$ from $- 4$ .

$\frac{14 - 2 - - 6}{7 - (- 2)}$

Step 2.1.4

Multiply $- 1$ by $- 6$ .

$\frac{14 - 2 + 6}{7 - (- 2)}$

Step 2.1.5

Subtract $2$ from $14$ .

$\frac{12 + 6}{7 - (- 2)}$

Step 2.1.6

Add $12$ and $6$ .

$\frac{18}{7 - (- 2)}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $- 2$ .

$\frac{18}{7 + 2}$

Step 2.2.2

Add $7$ and $2$ .

$\frac{18}{9}$

Step 2.3

Divide $18$ by $9$ .

$2$