Find the Difference Quotient f(x)=7x+7

$f (x) = 7 x + 7$

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.

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

Simplify the result.

Apply the distributive property.

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

The final answer is $7 x + 7 h + 7$ .

$7 x + 7 h + 7$

Reorder $7 x$ and $7 h$ .

$7 h + 7 x + 7$

Find the components of the definition.

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

$f (x) = 7 x + 7$

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

$f (x) = 7 x + 7$

Step 3

Plug in the components.

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

Step 4

Simplify.

Simplify the numerator.

Factor $7$ out of $7 x + 7$ .

Factor $7$ out of $7 x$ .

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

Factor $7$ out of $7$ .

$\frac{7 h + 7 x + 7 - (7 (x) + 7 (1))}{h}$

Factor $7$ out of $7 (x) + 7 (1)$ .

$\frac{7 h + 7 x + 7 - (7 (x + 1))}{h}$

$\frac{7 h + 7 x + 7 - 1 \cdot 7 (x + 1)}{h}$

Multiply $- 1$ by $7$ .

$\frac{7 h + 7 x + 7 - 7 (x + 1)}{h}$

Factor $7$ out of $7 h + 7 x + 7 - 7 (x + 1)$ .

Factor $7$ out of $7 h$ .

$\frac{7 h + 7 x + 7 - 7 (x + 1)}{h}$

Factor $7$ out of $7 x$ .

$\frac{7 h + 7 (x) + 7 - 7 (x + 1)}{h}$

Factor $7$ out of $7$ .

$\frac{7 h + 7 (x) + 7 (1) - 7 (x + 1)}{h}$

Factor $7$ out of $- 7 (x + 1)$ .

$\frac{7 h + 7 (x) + 7 (1) + 7 (- (x + 1))}{h}$

Factor $7$ out of $7 h + 7 (x)$ .

$\frac{7 (h + x) + 7 (1) + 7 (- (x + 1))}{h}$

Factor $7$ out of $7 (h + x) + 7 (1)$ .

$\frac{7 (h + x + 1) + 7 (- (x + 1))}{h}$

Factor $7$ out of $7 (h + x + 1) + 7 (- (x + 1))$ .

$\frac{7 (h + x + 1 - (x + 1))}{h}$

Apply the distributive property.

$\frac{7 (h + x + 1 - x - 1 \cdot 1)}{h}$

Multiply $- 1$ by $1$ .

$\frac{7 (h + x + 1 - x - 1)}{h}$

Subtract $x$ from $x$ .

$\frac{7 (h + 0 + 1 - 1)}{h}$

Add $h$ and $0$ .

$\frac{7 (h + 1 - 1)}{h}$

Subtract $1$ from $1$ .

$\frac{7 (h + 0)}{h}$

Add $h$ and $0$ .

$\frac{7 h}{h}$

Divide $7$ by $1$ .

$7$

Step 5

Find the Difference Quotient f(x)=7x+7

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