Find the Difference Quotient f(x)=-3x-7

$f (x) = - 3 x - 7$

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.

$f (x + h) = - 3 (x + h) - 7$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 3 x - 3 h - 7$

The final answer is $- 3 x - 3 h - 7$ .

$- 3 x - 3 h - 7$

Reorder $- 3 x$ and $- 3 h$ .

$- 3 h - 3 x - 7$

Find the components of the definition.

$f (x + h) = - 3 h - 3 x - 7$

$f (x) = - 3 x - 7$

$f (x + h) = - 3 h - 3 x - 7$

$f (x) = - 3 x - 7$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 3 h - 3 x - 7 - (- 3 x - 7)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{- 3 h - 3 x - 7 - (- 3 x) - - 7}{h}$

Multiply $- 3$ by $- 1$ .

$\frac{- 3 h - 3 x - 7 + 3 x - - 7}{h}$

Multiply $- 1$ by $- 7$ .

$\frac{- 3 h - 3 x - 7 + 3 x + 7}{h}$

Add $- 3 x$ and $3 x$ .

$\frac{- 3 h + 0 - 7 + 7}{h}$

Add $- 3 h$ and $0$ .

$\frac{- 3 h - 7 + 7}{h}$

Add $- 7$ and $7$ .

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

Add $- 3 h$ and $0$ .

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

Divide $- 3$ by $1$ .

$- 3$

Step 5