Find the Difference Quotient f(x)=3x+4

$f (x) = 3 x + 4$

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.

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

Simplify the result.

Apply the distributive property.

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

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

$3 x + 3 h + 4$

Reorder $3 x$ and $3 h$ .

$3 h + 3 x + 4$

Find the components of the definition.

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

$f (x) = 3 x + 4$

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

$f (x) = 3 x + 4$

Step 3

Plug in the components.

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

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $4$ .

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

Subtract $3 x$ from $3 x$ .

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

Add $3 h$ and $0$ .

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

Subtract $4$ from $4$ .

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

Add $3 h$ and $0$ .

$\frac{3 h}{h}$

Divide $3$ by $1$ .

$3$

Step 5