Precalculus Examples

$y = 3 x + 4$ , $[2, 3]$

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.

$\frac{f (3) - f (2)}{(3) - (2)}$

Step 1.2

Substitute the equation $y = 3 x + 4$ for $f (3)$ and $f (2)$ , replacing $x$ in the function with the corresponding $x$ value.

$\frac{(3 (3) + 4) - (3 (2) + 4)}{(3) - (2)}$

Step 2

Simplify the expression.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $3$ by $3$ .

$\frac{9 + 4 - (3 (2) + 4)}{3 - (2)}$

Step 2.1.2

Multiply $3$ by $2$ .

$\frac{9 + 4 - (6 + 4)}{3 - (2)}$

Step 2.1.3

Add $6$ and $4$ .

$\frac{9 + 4 - 1 \cdot 10}{3 - (2)}$

Step 2.1.4

Multiply $- 1$ by $10$ .

$\frac{9 + 4 - 10}{3 - (2)}$

Step 2.1.5

Add $9$ and $4$ .

$\frac{13 - 10}{3 - (2)}$

Step 2.1.6

Subtract $10$ from $13$ .

$\frac{3}{3 - (2)}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $2$ .

$\frac{3}{3 - 2}$

Step 2.2.2

Subtract $2$ from $3$ .

$\frac{3}{1}$

Step 2.3

Divide $3$ by $1$ .

$3$