Precalculus Examples

$y = 3 - | x |$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 3 - | x |$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $3 - | x | = 0$ .

$3 - | x | = 0$

Step 1.2.2

Subtract $3$ from both sides of the equation.

$- | x | = - 3$

Step 1.2.3

Divide each term in $- | x | = - 3$ by $- 1$ and simplify.

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Step 1.2.3.1

Divide each term in $- | x | = - 3$ by $- 1$ .

$\frac{- | x |}{- 1} = \frac{- 3}{- 1}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{| x |}{1} = \frac{- 3}{- 1}$

Step 1.2.3.2.2

Divide $| x |$ by $1$ .

$| x | = \frac{- 3}{- 1}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 3$ by $- 1$ .

$| x | = 3$

Step 1.2.4

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm 3$

Step 1.2.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.2.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Step 1.2.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

Step 1.2.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 3 - | 0 |$

Step 2.2

Simplify $3 - | 0 |$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

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

$y = 3 - 0$

Step 2.2.1.2

Multiply $- 1$ by $0$ .

$y = 3 + 0$

Step 2.2.2

Add $3$ and $0$ .

$y = 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 3, 0)$

y-intercept(s): $(0, 3)$

Step 4