Find the Difference Quotient f(x)=-8x+1

$f (x) = - 8 x + 1$

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.

$f (x + h) = - 8 (x + h) + 1$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 8 x - 8 h + 1$

The final answer is $- 8 x - 8 h + 1$ .

$- 8 x - 8 h + 1$

Reorder $- 8 x$ and $- 8 h$ .

$- 8 h - 8 x + 1$

Find the components of the definition.

$f (x + h) = - 8 h - 8 x + 1$

$f (x) = - 8 x + 1$

$f (x + h) = - 8 h - 8 x + 1$

$f (x) = - 8 x + 1$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 8 h - 8 x + 1 - (- 8 x + 1)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{- 8 h - 8 x + 1 - (- 8 x) - 1 \cdot 1}{h}$

Multiply $- 8$ by $- 1$ .

$\frac{- 8 h - 8 x + 1 + 8 x - 1 \cdot 1}{h}$

Multiply $- 1$ by $1$ .

$\frac{- 8 h - 8 x + 1 + 8 x - 1}{h}$

Add $- 8 x$ and $8 x$ .

$\frac{- 8 h + 0 + 1 - 1}{h}$

Add $- 8 h$ and $0$ .

$\frac{- 8 h + 1 - 1}{h}$

Subtract $1$ from $1$ .

$\frac{- 8 h + 0}{h}$

Add $- 8 h$ and $0$ .

$\frac{- 8 h}{h}$

Divide $- 8$ by $1$ .

$- 8$

Step 5