Precalculus Examples

$r (a) = 5 a$

Step 1

Consider the difference quotient formula.

$\frac{f (a + h) - f a}{h}$

Step 2

Find the components of the definition.

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Step 2.1

Evaluate the function at $x = a + h$ .

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Step 2.1.1

Replace the variable $a$ with $a + h$ in the expression.

$r (a + h) = 5 (a + h)$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Apply the distributive property.

$r (a + h) = 5 a + 5 h$

Step 2.1.2.2

The final answer is $5 a + 5 h$ .

$5 a + 5 h$

Step 2.2

Find the components of the definition.

$r (a + h) = 5 a + 5 h$

$r (a) = 5 a$

$r (a + h) = 5 a + 5 h$

$r (a) = 5 a$

Step 3

Plug in the components.

$\frac{r (a + h) - r a}{h} = \frac{5 a + 5 h - (5 a)}{h}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $5$ .

$\frac{5 a + 5 h - 5 a}{h}$

Step 4.1.2

Subtract $5 a$ from $5 a$ .

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

Step 4.1.3

Add $5 h$ and $0$ .

$\frac{5 h}{h}$

Step 4.2

Cancel the common factor of $h$ .

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Step 4.2.1

Cancel the common factor.

$\frac{5 h}{h}$

Step 4.2.2

Divide $5$ by $1$ .

$5$

Step 5