Precalculus Examples

$f (x) = 4 x - 2$ , $(1, 2)$ , $(0, - 2)$

Substitute using the average rate of change formula.

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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.

$\frac{f (1) - f (0)}{(1) - (0)}$

Substitute the equation $y = 4 x - 2$ for $f (1)$ and $f (0)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(4 (1) - 2) - (4 (0) - 2)}{(1) - (0)}$

Simplify the expression.

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Simplify the numerator.

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Multiply $4$ by $1$ .

$\frac{4 - 2 - (4 (0) - 2)}{(1) - (0)}$

Multiply $4$ by $0$ .

$\frac{4 - 2 - (0 - 2)}{(1) - (0)}$

Subtract $2$ from $0$ .

$\frac{4 - 2 - - 2}{(1) - (0)}$

Multiply $- 1$ by $- 2$ .

$\frac{4 - 2 + 2}{(1) - (0)}$

Subtract $2$ from $4$ .

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

Add $2$ and $2$ .

$\frac{4}{(1) - (0)}$

Simplify the denominator.

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Multiply $- 1$ by $0$ .

$\frac{4}{1 + 0}$

Add $1$ and $0$ .

$\frac{4}{1}$

Divide $4$ by $1$ .

$4$

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