Precalculus Examples

$y = {1.2}^{(x + 4)} - 2$

Step 1

Write $y = {1.2}^{(x + 4)} - 2$ as a function.

$f (x) = {1.2}^{(x + 4)} - 2$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$f (x + h) = {1.2}^{(x + h) + 4} - 2$

Step 3.1.2

Simplify the result.

Tap for more steps...

Step 3.1.2.1

Remove parentheses.

$f (x + h) = {1.2}^{x + h + 4} - 2$

Step 3.1.2.2

The final answer is ${1.2}^{x + h + 4} - 2$ .

${1.2}^{x + h + 4} - 2$

Step 3.2

Find the components of the definition.

$f (x + h) = {1.2}^{x + h + 4} - 2$

$f (x) = {1.2}^{x + 4} - 2$

$f (x + h) = {1.2}^{x + h + 4} - 2$

$f (x) = {1.2}^{x + 4} - 2$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{{1.2}^{x + h + 4} - 2 - ({1.2}^{x + 4} - 2)}{h}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{{1.2}^{x + h + 4} - 2 - {1.2}^{x + 4} - - 2}{h}$

Step 5.2

Multiply $- 1$ by $- 2$ .

$\frac{{1.2}^{x + h + 4} - 2 - {1.2}^{x + 4} + 2}{h}$

Step 5.3

Add $- 2$ and $2$ .

$\frac{{1.2}^{x + h + 4} + 0 - {1.2}^{x + 4}}{h}$

Step 5.4

Add ${1.2}^{x + h + 4}$ and $0$ .

$\frac{{1.2}^{x + h + 4} - {1.2}^{x + 4}}{h}$

Step 6