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

$f (x) = 8 x + 10$

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.

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

Simplify the result.

Apply the distributive property.

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

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

$8 x + 8 h + 10$

Reorder $8 x$ and $8 h$ .

$8 h + 8 x + 10$

Find the components of the definition.

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

$f (x) = 8 x + 10$

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

$f (x) = 8 x + 10$

Step 3

Plug in the components.

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

Step 4

Simplify.

Simplify the numerator.

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

Factor $2$ out of $8 x$ .

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

Factor $2$ out of $10$ .

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

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

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

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

Multiply $- 1$ by $2$ .

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

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

Factor $2$ out of $8 h$ .

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

Factor $2$ out of $8 x$ .

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

Factor $2$ out of $10$ .

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

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

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

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

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

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

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

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

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

Apply the distributive property.

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $4 x$ from $4 x$ .

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

Add $4 h$ and $0$ .

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

Subtract $5$ from $5$ .

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

Add $4 h$ and $0$ .

$\frac{2 \cdot 4 h}{h}$

Multiply $2$ by $4$ .

$\frac{8 h}{h}$

Divide $8$ by $1$ .

$8$

Step 5

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

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