Find the Difference Quotient f(x)=-10x+8

$f (x) = - 10 x + 8$

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.

$f (x + h) = - 10 (x + h) + 8$

Simplify the result.

Apply the distributive property.

$f (x + h) = - 10 x - 10 h + 8$

The final answer is $- 10 x - 10 h + 8$ .

$- 10 x - 10 h + 8$

Reorder $- 10 x$ and $- 10 h$ .

$- 10 h - 10 x + 8$

Find the components of the definition.

$f (x + h) = - 10 h - 10 x + 8$

$f (x) = - 10 x + 8$

$f (x + h) = - 10 h - 10 x + 8$

$f (x) = - 10 x + 8$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 10 h - 10 x + 8 - (- 10 x + 8)}{h}$

Step 4

Simplify.

Simplify the numerator.

Factor $2$ out of $- 10 x + 8$ .

Factor $2$ out of $- 10 x$ .

$\frac{- 10 h - 10 x + 8 - (2 (- 5 x) + 8)}{h}$

Factor $2$ out of $8$ .

$\frac{- 10 h - 10 x + 8 - (2 (- 5 x) + 2 (4))}{h}$

Factor $2$ out of $2 (- 5 x) + 2 (4)$ .

$\frac{- 10 h - 10 x + 8 - (2 (- 5 x + 4))}{h}$

$\frac{- 10 h - 10 x + 8 - 1 \cdot 2 (- 5 x + 4)}{h}$

Multiply $- 1$ by $2$ .

$\frac{- 10 h - 10 x + 8 - 2 (- 5 x + 4)}{h}$

Factor $2$ out of $- 10 h - 10 x + 8 - 2 (- 5 x + 4)$ .

Factor $2$ out of $- 10 h$ .

$\frac{2 (- 5 h) - 10 x + 8 - 2 (- 5 x + 4)}{h}$

Factor $2$ out of $- 10 x$ .

$\frac{2 (- 5 h) + 2 (- 5 x) + 8 - 2 (- 5 x + 4)}{h}$

Factor $2$ out of $8$ .

$\frac{2 (- 5 h) + 2 (- 5 x) + 2 (4) - 2 (- 5 x + 4)}{h}$

Factor $2$ out of $- 2 (- 5 x + 4)$ .

$\frac{2 (- 5 h) + 2 (- 5 x) + 2 (4) + 2 (- (- 5 x + 4))}{h}$

Factor $2$ out of $2 (- 5 h) + 2 (- 5 x)$ .

$\frac{2 (- 5 h - 5 x) + 2 (4) + 2 (- (- 5 x + 4))}{h}$

Factor $2$ out of $2 (- 5 h - 5 x) + 2 (4)$ .

$\frac{2 (- 5 h - 5 x + 4) + 2 (- (- 5 x + 4))}{h}$

Factor $2$ out of $2 (- 5 h - 5 x + 4) + 2 (- (- 5 x + 4))$ .

$\frac{2 (- 5 h - 5 x + 4 - (- 5 x + 4))}{h}$

Apply the distributive property.

$\frac{2 (- 5 h - 5 x + 4 - (- 5 x) - 1 \cdot 4)}{h}$

Multiply $- 5$ by $- 1$ .

$\frac{2 (- 5 h - 5 x + 4 + 5 x - 1 \cdot 4)}{h}$

Multiply $- 1$ by $4$ .

$\frac{2 (- 5 h - 5 x + 4 + 5 x - 4)}{h}$

Add $- 5 x$ and $5 x$ .

$\frac{2 (- 5 h + 0 + 4 - 4)}{h}$

Add $- 5 h$ and $0$ .

$\frac{2 (- 5 h + 4 - 4)}{h}$

Subtract $4$ from $4$ .

$\frac{2 (- 5 h + 0)}{h}$

Add $- 5 h$ and $0$ .

$\frac{2 \cdot - 5 h}{h}$

Multiply $2$ by $- 5$ .

$\frac{- 10 h}{h}$

Divide $- 10$ by $1$ .

$- 10$

Step 5

Find the Difference Quotient f(x)=-10x+8

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