Precalculus Examples

$f (x) = x$ , $x = 0$

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

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

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

Simplify the result.

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Remove parentheses.

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

The final answer is $x + h$ .

$x + h$

Find the components of the definition.

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

$f (x) = x$

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

$f (x) = x$

Step 3

Plug in the components.

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

Step 4

Simplify.

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Simplify the numerator.

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Subtract $x$ from $x$ .

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

Add $h$ and $0$ .

$\frac{h}{h}$

Rewrite the expression.

$1$

Step 5

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