Find the Difference Quotient f(x)=8x+9

$f (x) = 8 x + 9$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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

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

$f (x + h) = 8 (x + h) + 9$

Simplify the result.

Apply the distributive property.

$f (x + h) = 8 x + 8 h + 9$

The final answer is $8 x + 8 h + 9$ .

$8 x + 8 h + 9$

Reorder $8 x$ and $8 h$ .

$8 h + 8 x + 9$

Find the components of the definition.

$f (x + h) = 8 h + 8 x + 9$

$f (x) = 8 x + 9$

$f (x + h) = 8 h + 8 x + 9$

$f (x) = 8 x + 9$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{8 h + 8 x + 9 - (8 x + 9)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{8 h + 8 x + 9 - (8 x) - 1 \cdot 9}{h}$

Multiply $8$ by $- 1$ .

$\frac{8 h + 8 x + 9 - 8 x - 1 \cdot 9}{h}$

Multiply $- 1$ by $9$ .

$\frac{8 h + 8 x + 9 - 8 x - 9}{h}$

Subtract $8 x$ from $8 x$ .

$\frac{8 h + 0 + 9 - 9}{h}$

Add $8 h$ and $0$ .

$\frac{8 h + 9 - 9}{h}$

Subtract $9$ from $9$ .

$\frac{8 h + 0}{h}$

Add $8 h$ and $0$ .

$\frac{8 h}{h}$

Divide $8$ by $1$ .

$8$

Step 5