Finite Math Examples

$f (x) = x^{2} + x - 3$ , $(5, 6)$

Step 1

Write $f (x) = x^{2} + x - 3$ as an equation.

$y = x^{2} + x - 3$

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

$\frac{f (6) - f (5)}{(6) - (5)}$

Step 2.2

Substitute the equation $y = x^{2} + x - 3$ for $f (6)$ and $f (5)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{{(6)}^{2} + 6 - 3 - ({(5)}^{2} + 5 - 3)}{(6) - (5)}$

Step 3

Simplify the expression.

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Step 3.1

Remove parentheses.

$\frac{{(6)}^{2} + 6 - 3 - ({(5)}^{2} + 5 - 3)}{(6) - (5)}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Raise $6$ to the power of $2$ .

$\frac{36 + 6 - 3 - (5^{2} + 5 - 3)}{6 - (5)}$

Step 3.2.2

Raise $5$ to the power of $2$ .

$\frac{36 + 6 - 3 - (25 + 5 - 3)}{6 - (5)}$

Step 3.2.3

Add $25$ and $5$ .

$\frac{36 + 6 - 3 - (30 - 3)}{6 - (5)}$

Step 3.2.4

Subtract $3$ from $30$ .

$\frac{36 + 6 - 3 - 1 \cdot 27}{6 - (5)}$

Step 3.2.5

Multiply $- 1$ by $27$ .

$\frac{36 + 6 - 3 - 27}{6 - (5)}$

Step 3.2.6

Add $36$ and $6$ .

$\frac{42 - 3 - 27}{6 - (5)}$

Step 3.2.7

Subtract $3$ from $42$ .

$\frac{39 - 27}{6 - (5)}$

Step 3.2.8

Subtract $27$ from $39$ .

$\frac{12}{6 - (5)}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

Multiply $- 1$ by $5$ .

$\frac{12}{6 - 5}$

Step 3.3.2

Subtract $5$ from $6$ .

$\frac{12}{1}$

Step 3.4

Divide $12$ by $1$ .

$12$