Find @FORMULA f(x)=4x+3

$f (x) = 4 x + 3$

Consider the difference quotient formula.

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

Find the components of the definition.

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

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

$f (x + h) = 4 (x + h) + 3$

Simplify the result.

Apply the distributive property.

$f (x + h) = 4 x + 4 h + 3$

The final answer is $4 x + 4 h + 3$ .

$4 x + 4 h + 3$

Reorder $4 x$ and $4 h$ .

$4 h + 4 x + 3$

Find the components of the definition.

$f (x + h) = 4 h + 4 x + 3$

$f (x) = 4 x + 3$

$f (x + h) = 4 h + 4 x + 3$

$f (x) = 4 x + 3$

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{4 h + 4 x + 3 - (4 x + 3)}{h}$

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{4 h + 4 x + 3 - (4 x) - 1 \cdot 3}{h}$

Multiply $4$ by $- 1$ .

$\frac{4 h + 4 x + 3 - 4 x - 1 \cdot 3}{h}$

Multiply $- 1$ by $3$ .

$\frac{4 h + 4 x + 3 - 4 x - 3}{h}$

Subtract $4 x$ from $4 x$ .

$\frac{4 h + 0 + 3 - 3}{h}$

Add $4 h$ and $0$ .

$\frac{4 h + 3 - 3}{h}$

Subtract $3$ from $3$ .

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

Add $4 h$ and $0$ .

$\frac{4 h}{h}$

Divide $4$ by $1$ .

$4$