Precalculus Examples

$\frac{7}{9}$

Step 1

Write $\frac{7}{9}$ as a function.

$f (x) = \frac{7}{9}$

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.

$f (x + h) = \frac{7}{9}$

Step 3.1.2

The final answer is $\frac{7}{9}$ .

$\frac{7}{9}$

Step 3.2

Find the components of the definition.

$f (x + h) = \frac{7}{9}$

$f (x) = \frac{7}{9}$

$f (x + h) = \frac{7}{9}$

$f (x) = \frac{7}{9}$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{\frac{7}{9} - (\frac{7}{9})}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Combine the numerators over the common denominator.

$\frac{\frac{7 - 7}{9}}{h}$

Step 5.1.2

Subtract $7$ from $7$ .

$\frac{\frac{0}{9}}{h}$

Step 5.1.3

Divide $0$ by $9$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6