Find Three Ordered Pair Solutions g(x)=3/4|x|

$g (x) = \frac{3}{4} | x |$

Step 1

Write $g (x) = \frac{3}{4} | x |$ as an equation.

$y = \frac{3}{4} | x |$

Step 2

Combine $\frac{3}{4}$ and $| x |$ .

$y = \frac{3 | x |}{4}$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

Simplify $\frac{3 | 0 |}{4}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = \frac{3 \cdot 0}{4}$

Multiply $3$ by $0$ .

$y = \frac{0}{4}$

Divide $0$ by $4$ .

$y = 0$

Use the $x$ and $y$ values to form the ordered pair.

$(0, 0)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

Simplify $\frac{3 | 1 |}{4}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$y = \frac{3 \cdot 1}{4}$

Multiply $3$ by $1$ .

$y = \frac{3}{4}$

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{3}{4})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

Simplify $\frac{3 | 2 |}{4}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$y = \frac{3 \cdot 2}{4}$

Multiply $3$ by $2$ .

$y = \frac{6}{4}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{3}{2}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{3}{2})$

Step 7

These are three possible solutions to the equation.

$(0, 0), (1, \frac{3}{4}), (2, \frac{3}{2})$

Step 8

Find Three Ordered Pair Solutions g(x)=3/4|x|

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