Find the Difference Quotient f(x)=9x-4

$f (x) = 9 x - 4$

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.

$f (x + h) = 9 (x + h) - 4$

Simplify the result.

Apply the distributive property.

$f (x + h) = 9 x + 9 h - 4$

The final answer is $9 x + 9 h - 4$ .

$9 x + 9 h - 4$

Reorder $9 x$ and $9 h$ .

$9 h + 9 x - 4$

Find the components of the definition.

$f (x + h) = 9 h + 9 x - 4$

$f (x) = 9 x - 4$

$f (x + h) = 9 h + 9 x - 4$

$f (x) = 9 x - 4$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{9 h + 9 x - 4 - (9 x - 4)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{9 h + 9 x - 4 - (9 x) - - 4}{h}$

Multiply $9$ by $- 1$ .

$\frac{9 h + 9 x - 4 - 9 x - - 4}{h}$

Multiply $- 1$ by $- 4$ .

$\frac{9 h + 9 x - 4 - 9 x + 4}{h}$

Subtract $9 x$ from $9 x$ .

$\frac{9 h + 0 - 4 + 4}{h}$

Add $9 h$ and $0$ .

$\frac{9 h - 4 + 4}{h}$

Add $- 4$ and $4$ .

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

Add $9 h$ and $0$ .

$\frac{9 h}{h}$

Divide $9$ by $1$ .

$9$

Step 5