Precalculus Examples

f (x) = 4 x - 2

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

(1, 2)

$(1, 2)$ ,

(0, - 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

$y$ values of the two points divided by the change in

x

$x$ values of the two points.

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

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

Step 1.2

Substitute the equation

y = 4 x - 2

$y = 4 x - 2$ for

f (1)

$f (1)$ and

f (0)

$f (0)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

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

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

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

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

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

$4$ by

1

$1$ .

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

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

Step 2.1.2

Multiply

4

$4$ by

0

$0$ .

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

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

Step 2.1.3

Subtract

2

$2$ from

0

$0$ .

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

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

Step 2.1.4

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

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

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

Step 2.1.5

Subtract

2

$2$ from

4

$4$ .

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

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

Step 2.1.6

Add

2

$2$ and

2

$2$ .

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

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

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

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

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

\frac{4}{1 + 0}

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

Step 2.2.2

Add

1

$1$ and

0

$0$ .

\frac{4}{1}

$\frac{4}{1}$

\frac{4}{1}

$\frac{4}{1}$

Step 2.3

Divide

4

$4$ by

1

$1$ .

4

$4$

4

$4$

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