Precalculus Examples

$y = | x - 6 |$

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 $x$ .

$0 = | x - 6 |$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $| x - 6 | = 0$ .

$| x - 6 | = 0$

Step 1.2.2

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

$x - 6 = \pm 0$

Step 1.2.3

Plus or minus $0$ is $0$ .

$x - 6 = 0$

Step 1.2.4

Add $6$ to both sides of the equation.

$x = 6$

Step 1.2.5

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

$x - 6 = \pm 0$

Step 1.2.6

Plus or minus $0$ is $0$ .

$x - 6 = 0$

Step 1.2.7

Add $6$ to both sides of the equation.

$x = 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(6, 0)$

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 $y$ .

$y = | (0) - 6 |$

Step 2.2

Simplify $| (0) - 6 |$ .

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Step 2.2.1

Subtract $6$ from $0$ .

$y = | - 6 |$

Step 2.2.2

The absolute value is the distance between a number and zero. The distance between $- 6$ and $0$ is $6$ .

$y = 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 6)$

Step 3

List the intersections.

x-intercept(s): $(6, 0)$

y-intercept(s): $(0, 6)$

Step 4