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Precalculus Examples

f (x) = \frac{1}{2} x + 3 x - 7

$f (x) = \frac{1}{2} x + 3 x - 7$

Step 1

Rewrite the function as an equation.

y = \frac{1}{2} x + 3 x - 7

$y = \frac{1}{2} x + 3 x - 7$

Step 2

Simplify

\frac{1}{2} x + 3 x - 7

$\frac{1}{2} x + 3 x - 7$ .

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Step 2.1

Combine

\frac{1}{2}

$\frac{1}{2}$ and

x

$x$ .

y = \frac{x}{2} + 3 x - 7

$y = \frac{x}{2} + 3 x - 7$

Step 2.2

To write

3 x

$3 x$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

y = \frac{x}{2} + 3 x \cdot \frac{2}{2} - 7

$y = \frac{x}{2} + 3 x \cdot \frac{2}{2} - 7$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine

3 x

$3 x$ and

\frac{2}{2}

$\frac{2}{2}$ .

y = \frac{x}{2} + \frac{3 x \cdot 2}{2} - 7

$y = \frac{x}{2} + \frac{3 x \cdot 2}{2} - 7$

Step 2.3.2

Combine the numerators over the common denominator.

y = \frac{x + 3 x \cdot 2}{2} - 7

$y = \frac{x + 3 x \cdot 2}{2} - 7$

y = \frac{x + 3 x \cdot 2}{2} - 7

$y = \frac{x + 3 x \cdot 2}{2} - 7$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor

x

$x$ out of

x + 3 x \cdot 2

$x + 3 x \cdot 2$ .

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Step 2.4.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

y = \frac{x^{1} + 3 x \cdot 2}{2} - 7

$y = \frac{x^{1} + 3 x \cdot 2}{2} - 7$

Step 2.4.1.1.2

Factor

x

$x$ out of

x^{1}

$x^{1}$ .

y = \frac{x \cdot 1 + 3 x \cdot 2}{2} - 7

$y = \frac{x \cdot 1 + 3 x \cdot 2}{2} - 7$

Step 2.4.1.1.3

Factor

x

$x$ out of

3 x \cdot 2

$3 x \cdot 2$ .

y = \frac{x \cdot 1 + x (3 \cdot 2)}{2} - 7

$y = \frac{x \cdot 1 + x (3 \cdot 2)}{2} - 7$

Step 2.4.1.1.4

Factor

x

$x$ out of

x \cdot 1 + x (3 \cdot 2)

$x \cdot 1 + x (3 \cdot 2)$ .

y = \frac{x (1 + 3 \cdot 2)}{2} - 7

$y = \frac{x (1 + 3 \cdot 2)}{2} - 7$

y = \frac{x (1 + 3 \cdot 2)}{2} - 7

$y = \frac{x (1 + 3 \cdot 2)}{2} - 7$

Step 2.4.1.2

Multiply

3

$3$ by

2

$2$ .

y = \frac{x (1 + 6)}{2} - 7

$y = \frac{x (1 + 6)}{2} - 7$

Step 2.4.1.3

Add

1

$1$ and

6

$6$ .

y = \frac{x \cdot 7}{2} - 7

$y = \frac{x \cdot 7}{2} - 7$

y = \frac{x \cdot 7}{2} - 7

$y = \frac{x \cdot 7}{2} - 7$

Step 2.4.2

Move

7

$7$ to the left of

x

$x$ .

y = \frac{7 x}{2} - 7

$y = \frac{7 x}{2} - 7$

y = \frac{7 x}{2} - 7

$y = \frac{7 x}{2} - 7$

y = \frac{7 x}{2} - 7

$y = \frac{7 x}{2} - 7$

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

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