Precalculus Examples

$f (x) = 5 x + 7$ from $x_{1} = - 1$ to $x_{2} = 0$

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.

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

Step 1.2

Substitute the equation $y = 5 x + 7$ for $f (0)$ and $f (- 1)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(5 (0) + 7) - (5 (- 1) + 7)}{(0) - (- 1)}$

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $5$ by $0$ .

$\frac{0 + 7 - (5 (- 1) + 7)}{0 - (- 1)}$

Step 2.1.2

Multiply $5$ by $- 1$ .

$\frac{0 + 7 - (- 5 + 7)}{0 - (- 1)}$

Step 2.1.3

Add $- 5$ and $7$ .

$\frac{0 + 7 - 1 \cdot 2}{0 - (- 1)}$

Step 2.1.4

Multiply $- 1$ by $2$ .

$\frac{0 + 7 - 2}{0 - (- 1)}$

Step 2.1.5

Add $0$ and $7$ .

$\frac{7 - 2}{0 - (- 1)}$

Step 2.1.6

Subtract $2$ from $7$ .

$\frac{5}{0 - (- 1)}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$\frac{5}{0 + 1}$

Step 2.2.2

Add $0$ and $1$ .

$\frac{5}{1}$

Step 2.3

Divide $5$ by $1$ .

$5$