Precalculus Examples

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

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.

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

Step 1.2

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

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

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $4$ by $1$ .

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

Step 2.1.2

Multiply $4$ by $0$ .

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

Step 2.1.3

Subtract $2$ from $0$ .

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

Step 2.1.4

Multiply $- 1$ by $- 2$ .

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

Step 2.1.5

Subtract $2$ from $4$ .

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

Step 2.1.6

Add $2$ and $2$ .

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

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $0$ .

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

Step 2.2.2

Add $1$ and $0$ .

$\frac{4}{1}$

Step 2.3

Divide $4$ by $1$ .

$4$