Precalculus Examples

$Y = 3 - 4 x$

Step 1

Write $Y = 3 - 4 x$ as a function.

$f (x) = 3 - 4 x$

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.

$f (x + h) = 3 - 4 (x + h)$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Apply the distributive property.

$f (x + h) = 3 - 4 x - 4 h$

Step 3.1.2.2

The final answer is $3 - 4 x - 4 h$ .

$3 - 4 x - 4 h$

$3 - 4 x - 4 h$

$3 - 4 x - 4 h$

Step 3.2

Reorder.

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Step 3.2.1

Move $3$ .

$- 4 x - 4 h + 3$

Step 3.2.2

Reorder $- 4 x$ and $- 4 h$ .

$- 4 h - 4 x + 3$

$- 4 h - 4 x + 3$

Step 3.3

Find the components of the definition.

$f (x + h) = - 4 h - 4 x + 3$

$f (x) = 3 - 4 x$

$f (x + h) = - 4 h - 4 x + 3$

$f (x) = 3 - 4 x$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 4 h - 4 x + 3 - (3 - 4 x)}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Apply the distributive property.

$\frac{- 4 h - 4 x + 3 - 1 \cdot 3 - (- 4 x)}{h}$

Step 5.1.2

Multiply $- 1$ by $3$ .

$\frac{- 4 h - 4 x + 3 - 3 - (- 4 x)}{h}$

Step 5.1.3

Multiply $- 4$ by $- 1$ .

$\frac{- 4 h - 4 x + 3 - 3 + 4 x}{h}$

Step 5.1.4

Add $- 4 x$ and $4 x$ .

$\frac{- 4 h + 0 + 3 - 3}{h}$

Step 5.1.5

Add $- 4 h$ and $0$ .

$\frac{- 4 h + 3 - 3}{h}$

Step 5.1.6

Subtract $3$ from $3$ .

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

Step 5.1.7

Add $- 4 h$ and $0$ .

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

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

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 $1$ .

$- 4$

$- 4$

$- 4$

Step 6

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