Precalculus Examples

$f (X) = \frac{4}{3} x + 8$

Step 1

Consider the difference quotient formula.

$\frac{f (X + h) - f X}{h}$

Step 2

Find the components of the definition.

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Step 2.1

Evaluate the function at $x = X + h$ .

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Step 2.1.1

Replace the variable $X$ with $X + h$ in the expression.

$f (X + h) = \frac{4}{3} x + 8$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Combine $\frac{4}{3}$ and $x$ .

$f (X + h) = \frac{4 x}{3} + 8$

Step 2.1.2.2

The final answer is $\frac{4 x}{3} + 8$ .

$\frac{4 x}{3} + 8$

Step 2.2

Find the components of the definition.

$f (X + h) = \frac{4 x}{3} + 8$

$f (X) = \frac{4 x}{3} + 8$

$f (X + h) = \frac{4 x}{3} + 8$

$f (X) = \frac{4 x}{3} + 8$

Step 3

Plug in the components.

$\frac{f (X + h) - f X}{h} = \frac{\frac{4 x}{3} + 8 - (\frac{4 x}{3} + 8)}{h}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Apply the distributive property.

$\frac{\frac{4 x}{3} + 8 - \frac{4 x}{3} - 1 \cdot 8}{h}$

Step 4.1.2

Multiply $- 1$ by $8$ .

$\frac{\frac{4 x}{3} + 8 - \frac{4 x}{3} - 8}{h}$

Step 4.1.3

Subtract $\frac{4 x}{3}$ from $\frac{4 x}{3}$ .

$\frac{0 + 8 - 8}{h}$

Step 4.1.4

Add $0$ and $8$ .

$\frac{8 - 8}{h}$

Step 4.1.5

Subtract $8$ from $8$ .

$\frac{0}{h}$

Step 4.2

Divide $0$ by $h$ .

$0$

Step 5