Precalculus Examples

$F (x) = x + 4$

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.

$F (x + h) = (x + h) + 4$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Remove parentheses.

$F (x + h) = x + h + 4$

Step 2.1.2.2

The final answer is $x + h + 4$ .

$x + h + 4$

Step 2.2

Reorder $x$ and $h$ .

$h + x + 4$

Step 2.3

Find the components of the definition.

$F (x + h) = h + x + 4$

$F (x) = x + 4$

$F (x + h) = h + x + 4$

$F (x) = x + 4$

Step 3

Plug in the components.

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

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.

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

Step 4.1.2

Multiply $- 1$ by $4$ .

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

Step 4.1.3

Subtract $x$ from $x$ .

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

Step 4.1.4

Add $h$ and $0$ .

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

Step 4.1.5

Subtract $4$ from $4$ .

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

Step 4.1.6

Add $h$ and $0$ .

$\frac{h}{h}$

Step 4.2

Cancel the common factor of $h$ .

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Step 4.2.1

Cancel the common factor.

$\frac{h}{h}$

Step 4.2.2

Rewrite the expression.

$1$

Step 5