Precalculus Examples

$y = 4 x$

Step 1

Write $y = 4 x$ as a function.

$f (x) = 4 x$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Apply the distributive property.

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

Step 3.1.2.2

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

$4 x + 4 h$

Step 3.2

Find the components of the definition.

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

$f (x) = 4 x$

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

$f (x) = 4 x$

Step 4

Plug in the components.

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

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $4$ .

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

Step 5.1.2

Subtract $4 x$ from $4 x$ .

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

Step 5.1.3

Add $4 h$ and $0$ .

$\frac{4 h}{h}$

Step 5.2

Cancel the common factor of $h$ .

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Step 5.2.1

Cancel the common factor.

$\frac{4 h}{h}$

Step 5.2.2

Divide $4$ by $1$ .

$4$

Step 6