Find the Difference Quotient f(x)=-4x+8

$f (x) = - 4 x + 8$

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.

$f (x + h) = - 4 (x + h) + 8$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 4 x - 4 h + 8$

The final answer is $- 4 x - 4 h + 8$ .

$- 4 x - 4 h + 8$

Reorder $- 4 x$ and $- 4 h$ .

$- 4 h - 4 x + 8$

Find the components of the definition.

$f (x + h) = - 4 h - 4 x + 8$

$f (x) = - 4 x + 8$

$f (x + h) = - 4 h - 4 x + 8$

$f (x) = - 4 x + 8$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 4 h - 4 x + 8 - (- 4 x + 8)}{h}$

Step 4

Simplify.

Simplify the numerator.

Factor $4$ out of $- 4 x + 8$ .

Factor $4$ out of $- 4 x$ .

$\frac{- 4 h - 4 x + 8 - (4 (- x) + 8)}{h}$

Factor $4$ out of $8$ .

$\frac{- 4 h - 4 x + 8 - (4 (- x) + 4 (2))}{h}$

Factor $4$ out of $4 (- x) + 4 (2)$ .

$\frac{- 4 h - 4 x + 8 - (4 (- x + 2))}{h}$

$\frac{- 4 h - 4 x + 8 - 1 \cdot 4 (- x + 2)}{h}$

Multiply $- 1$ by $4$ .

$\frac{- 4 h - 4 x + 8 - 4 (- x + 2)}{h}$

Factor $4$ out of $- 4 h - 4 x + 8 - 4 (- x + 2)$ .

Factor $4$ out of $- 4 h$ .

$\frac{4 (- h) - 4 x + 8 - 4 (- x + 2)}{h}$

Factor $4$ out of $- 4 x$ .

$\frac{4 (- h) + 4 (- x) + 8 - 4 (- x + 2)}{h}$

Factor $4$ out of $8$ .

$\frac{4 (- h) + 4 (- x) + 4 (2) - 4 (- x + 2)}{h}$

Factor $4$ out of $- 4 (- x + 2)$ .

$\frac{4 (- h) + 4 (- x) + 4 (2) + 4 (- (- x + 2))}{h}$

Factor $4$ out of $4 (- h) + 4 (- x)$ .

$\frac{4 (- h - x) + 4 (2) + 4 (- (- x + 2))}{h}$

Factor $4$ out of $4 (- h - x) + 4 (2)$ .

$\frac{4 (- h - x + 2) + 4 (- (- x + 2))}{h}$

Factor $4$ out of $4 (- h - x + 2) + 4 (- (- x + 2))$ .

$\frac{4 (- h - x + 2 - (- x + 2))}{h}$

Apply the distributive property.

$\frac{4 (- h - x + 2 - - x - 1 \cdot 2)}{h}$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$\frac{4 (- h - x + 2 + 1 x - 1 \cdot 2)}{h}$

Multiply $x$ by $1$ .

$\frac{4 (- h - x + 2 + x - 1 \cdot 2)}{h}$

Multiply $- 1$ by $2$ .

$\frac{4 (- h - x + 2 + x - 2)}{h}$

Add $- x$ and $x$ .

$\frac{4 (- h + 0 + 2 - 2)}{h}$

Add $- h$ and $0$ .

$\frac{4 (- h + 2 - 2)}{h}$

Subtract $2$ from $2$ .

$\frac{4 (- h + 0)}{h}$

Add $- h$ and $0$ .

$\frac{4 \cdot - 1 h}{h}$

Combine exponents.

Factor out negative.

$\frac{- (4 h)}{h}$

Multiply $4$ by $- 1$ .

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

Divide $- 4$ by $1$ .

$- 4$

Step 5

Find the Difference Quotient f(x)=-4x+8

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