Precalculus Examples

$x + y = - 5$

Step 1

Write $y = - 5 - x$ as a function.

$f (x) = - 5 - x$

Step 2

Subtract $x$ from both sides of the equation.

$y = - 5 - x$

Step 3

Consider the difference quotient formula.

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

Step 4

Find the components of the definition.

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Step 4.1

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

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Step 4.1.1

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

$f (x + h) = - 5 - (x + h)$

Step 4.1.2

Simplify the result.

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Step 4.1.2.1

Apply the distributive property.

$f (x + h) = - 5 - x - h$

Step 4.1.2.2

The final answer is $- 5 - x - h$ .

$- 5 - x - h$

$- 5 - x - h$

$- 5 - x - h$

Step 4.2

Reorder.

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Step 4.2.1

Move $- 5$ .

$- x - h - 5$

Step 4.2.2

Reorder $- x$ and $- h$ .

$- h - x - 5$

$- h - x - 5$

Step 4.3

Find the components of the definition.

$f (x + h) = - h - x - 5$

$f (x) = - 5 - x$

$f (x + h) = - h - x - 5$

$f (x) = - 5 - x$

Step 5

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- h - x - 5 - (- 5 - x)}{h}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Apply the distributive property.

$\frac{- h - x - 5 - - 5 - - x}{h}$

Step 6.1.2

Multiply $- 1$ by $- 5$ .

$\frac{- h - x - 5 + 5 - - x}{h}$

Step 6.1.3

Multiply $- - x$ .

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Step 6.1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{- h - x - 5 + 5 + 1 x}{h}$

Step 6.1.3.2

Multiply $x$ by $1$ .

$\frac{- h - x - 5 + 5 + x}{h}$

$\frac{- h - x - 5 + 5 + x}{h}$

Step 6.1.4

Add $- x$ and $x$ .

$\frac{- h + 0 - 5 + 5}{h}$

Step 6.1.5

Add $- h$ and $0$ .

$\frac{- h - 5 + 5}{h}$

Step 6.1.6

Add $- 5$ and $5$ .

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

Step 6.1.7

Add $- h$ and $0$ .

$\frac{- h}{h}$

$\frac{- h}{h}$

Step 6.2

Cancel the common factor of $h$ .

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Step 6.2.1

Cancel the common factor.

$\frac{- h}{h}$

Step 6.2.2

Divide $- 1$ by $1$ .

$- 1$

$- 1$

$- 1$

Step 7

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$