Find @FORMULA f(x)=9x+10

$f (x) = 9 x + 10$

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.

$f (x + h) = 9 (x + h) + 10$

Simplify the result.

Apply the distributive property.

$f (x + h) = 9 x + 9 h + 10$

The final answer is $9 x + 9 h + 10$ .

$9 x + 9 h + 10$

Reorder $9 x$ and $9 h$ .

$9 h + 9 x + 10$

Find the components of the definition.

$f (x + h) = 9 h + 9 x + 10$

$f (x) = 9 x + 10$

$f (x + h) = 9 h + 9 x + 10$

$f (x) = 9 x + 10$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{9 h + 9 x + 10 - (9 x + 10)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{9 h + 9 x + 10 - (9 x) - 1 \cdot 10}{h}$

Multiply $9$ by $- 1$ .

$\frac{9 h + 9 x + 10 - 9 x - 1 \cdot 10}{h}$

Multiply $- 1$ by $10$ .

$\frac{9 h + 9 x + 10 - 9 x - 10}{h}$

Subtract $9 x$ from $9 x$ .

$\frac{9 h + 0 + 10 - 10}{h}$

Add $9 h$ and $0$ .

$\frac{9 h + 10 - 10}{h}$

Subtract $10$ from $10$ .

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

Add $9 h$ and $0$ .

$\frac{9 h}{h}$

Divide $9$ by $1$ .

$9$

Step 5