Precalculus Examples

$r (a) = 9 a$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$r (a + h) = 9 (a + h)$

Step 2.1.2

Simplify the result.

Tap for more steps...

Step 2.1.2.1

Apply the distributive property.

$r (a + h) = 9 a + 9 h$

Step 2.1.2.2

The final answer is $9 a + 9 h$ .

$9 a + 9 h$

Step 2.2

Find the components of the definition.

$r (a + h) = 9 a + 9 h$

$r (a) = 9 a$

$r (a + h) = 9 a + 9 h$

$r (a) = 9 a$

Step 3

Plug in the components.

$\frac{r (a + h) - r a}{h} = \frac{9 a + 9 h - (9 a)}{h}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $- 1$ by $9$ .

$\frac{9 a + 9 h - 9 a}{h}$

Step 4.1.2

Subtract $9 a$ from $9 a$ .

$\frac{9 h + 0}{h}$

Step 4.1.3

Add $9 h$ and $0$ .

$\frac{9 h}{h}$

Step 4.2

Cancel the common factor of $h$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{9 h}{h}$

Step 4.2.2

Divide $9$ by $1$ .

$9$

Step 5