Algebra Examples

f (x) = 6 x - 3

$f (x) = 6 x - 3$ ,

(1, 4)

$(1, 4)$

Step 1

Write

f (x) = 6 x - 3

$f (x) = 6 x - 3$ as an equation.

y = 6 x - 3

$y = 6 x - 3$

Step 2

Substitute using the average rate of change formula.

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Step 2.1

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 (4) - f (1)}{(4) - (1)}

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

Step 2.2

Substitute the equation

y = 6 x - 3

$y = 6 x - 3$ for

f (4)

$f (4)$ and

f (1)

$f (1)$ , replacing

x

$x$ in the function with the corresponding

x

$x$ value.

\frac{(6 (4) - 3) - (6 (1) - 3)}{(4) - (1)}

$\frac{(6 (4) - 3) - (6 (1) - 3)}{(4) - (1)}$

\frac{(6 (4) - 3) - (6 (1) - 3)}{(4) - (1)}

$\frac{(6 (4) - 3) - (6 (1) - 3)}{(4) - (1)}$

Step 3

Simplify the expression.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply

6

$6$ by

4

$4$ .

\frac{24 - 3 - (6 (1) - 3)}{4 - (1)}

$\frac{24 - 3 - (6 (1) - 3)}{4 - (1)}$

Step 3.1.2

Multiply

6

$6$ by

1

$1$ .

\frac{24 - 3 - (6 - 3)}{4 - (1)}

$\frac{24 - 3 - (6 - 3)}{4 - (1)}$

Step 3.1.3

Subtract

3

$3$ from

6

$6$ .

\frac{24 - 3 - 1 \cdot 3}{4 - (1)}

$\frac{24 - 3 - 1 \cdot 3}{4 - (1)}$

Step 3.1.4

Multiply

- 1

$- 1$ by

3

$3$ .

\frac{24 - 3 - 3}{4 - (1)}

$\frac{24 - 3 - 3}{4 - (1)}$

Step 3.1.5

Subtract

3

$3$ from

24

$24$ .

\frac{21 - 3}{4 - (1)}

$\frac{21 - 3}{4 - (1)}$

Step 3.1.6

Subtract

3

$3$ from

21

$21$ .

\frac{18}{4 - (1)}

$\frac{18}{4 - (1)}$

\frac{18}{4 - (1)}

$\frac{18}{4 - (1)}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Multiply

- 1

$- 1$ by

1

$1$ .

\frac{18}{4 - 1}

$\frac{18}{4 - 1}$

Step 3.2.2

Subtract

1

$1$ from

4

$4$ .

\frac{18}{3}

$\frac{18}{3}$

\frac{18}{3}

$\frac{18}{3}$

Step 3.3

Divide

18

$18$ by

3

$3$ .

6

$6$

6

$6$

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