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.

Tap for more steps...

Step 2.1

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

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Apply the distributive property.

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

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

Add $- 4$ and $4$ .

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

Step 4.1.6

Add $h$ and $0$ .

$\frac{h}{h}$

Step 4.2

Cancel the common factor of $h$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\frac{h}{h}$

Step 4.2.2

Rewrite the expression.

$1$

Step 5