Find the Difference Quotient f(x)=1/4x+7

$f (x) = \frac{1}{4} x + 7$

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.

$f (x + h) = \frac{1}{4} \cdot (x + h) + 7$

Simplify the result.

Simplify each term.

Apply the distributive property.

$f (x + h) = \frac{1}{4} x + \frac{1}{4} h + 7$

Combine $\frac{1}{4}$ and $x$ .

$f (x + h) = \frac{x}{4} + \frac{1}{4} h + 7$

Combine $\frac{1}{4}$ and $h$ .

$f (x + h) = \frac{x}{4} + \frac{h}{4} + 7$

The final answer is $\frac{x}{4} + \frac{h}{4} + 7$ .

$\frac{x}{4} + \frac{h}{4} + 7$

Reorder $\frac{x}{4}$ and $\frac{h}{4}$ .

$\frac{h}{4} + \frac{x}{4} + 7$

Find the components of the definition.

$f (x + h) = \frac{h}{4} + \frac{x}{4} + 7$

$f (x) = \frac{x}{4} + 7$

$f (x + h) = \frac{h}{4} + \frac{x}{4} + 7$

$f (x) = \frac{x}{4} + 7$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{\frac{h}{4} + \frac{x}{4} + 7 - (\frac{x}{4} + 7)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{\frac{h}{4} + \frac{x}{4} + 7 - \frac{x}{4} - 1 \cdot 7}{h}$

Multiply $- 1$ by $7$ .

$\frac{\frac{h}{4} + \frac{x}{4} + 7 - \frac{x}{4} - 7}{h}$

Subtract $\frac{x}{4}$ from $\frac{x}{4}$ .

$\frac{\frac{h}{4} + 0 + 7 - 7}{h}$

Add $\frac{h}{4}$ and $0$ .

$\frac{\frac{h}{4} + 7 - 7}{h}$

Subtract $7$ from $7$ .

$\frac{\frac{h}{4} + 0}{h}$

Add $\frac{h}{4}$ and $0$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

Rewrite the expression.

$\frac{1}{4}$

Step 5

Find the Difference Quotient f(x)=1/4x+7

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