Algebra Examples

$y = \frac{1}{2} f (x)$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot (f (- 2))$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = \frac{1}{2} f \cdot - 2$

Step 2.2

Remove parentheses.

$y = \frac{1}{2} \cdot (f (- 2))$

Step 2.3

Simplify $\frac{1}{2} \cdot (f (- 2))$ .

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Factor $2$ out of $f (- 2)$ .

$y = \frac{1}{2} \cdot (2 (f \cdot (- 1)))$

Step 2.3.1.2

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 (f \cdot (- 1)))$

Step 2.3.1.3

Rewrite the expression.

$y = f \cdot (- 1)$

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Move $- 1$ to the left of $f$ .

$y = - 1 f$

Step 2.3.2.2

Rewrite $- 1 f$ as $- f$ .

$y = - f$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot (f (- 1))$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = \frac{1}{2} f \cdot - 1$

Step 4.2

Remove parentheses.

$y = \frac{1}{2} \cdot (f (- 1))$

Step 4.3

Simplify $\frac{1}{2} \cdot (f (- 1))$ .

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Step 4.3.1

Simplify the expression.

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Step 4.3.1.1

Move $- 1$ to the left of $f$ .

$y = \frac{1}{2} \cdot (- 1 f)$

Step 4.3.1.2

Rewrite $- 1 f$ as $- f$ .

$y = \frac{1}{2} \cdot (- f)$

Step 4.3.2

Combine $\frac{1}{2}$ and $f$ .

$y = - \frac{f}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot (f (0))$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{1}{2} f \cdot 0$

Step 6.2

Remove parentheses.

$y = \frac{1}{2} \cdot (f (0))$

Step 6.3

Simplify $\frac{1}{2} \cdot (f (0))$ .

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Step 6.3.1

Multiply $f$ by $0$ .

$y = \frac{1}{2} \cdot 0$

Step 6.3.2

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot (f (1))$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{1}{2} f \cdot 1$

Step 8.2

Remove parentheses.

$y = \frac{1}{2} \cdot (f (1))$

Step 8.3

Simplify $\frac{1}{2} \cdot (f (1))$ .

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Step 8.3.1

Multiply $f$ by $1$ .

$y = \frac{1}{2} \cdot f$

Step 8.3.2

Combine $\frac{1}{2}$ and $f$ .

$y = \frac{f}{2}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot (f (2))$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = \frac{1}{2} f \cdot 2$

Step 10.2

Remove parentheses.

$y = \frac{1}{2} \cdot (f (2))$

Step 10.3

Cancel the common factor of $2$ .

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Step 10.3.1

Factor $2$ out of $f (2)$ .

$y = \frac{1}{2} \cdot (2 f)$

Step 10.3.2

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 f)$

Step 10.3.3

Rewrite the expression.

$y = f$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - f \\ - 1 & - \frac{f}{2} \\ 0 & 0 \\ 1 & \frac{f}{2} \\ 2 & f \end{array}$

Step 12