Precalculus Examples

y = | x - 6 |

$y = | x - 6 |$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = | x - 6 |

$0 = | x - 6 |$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

| x - 6 | = 0

$| x - 6 | = 0$ .

| x - 6 | = 0

$| x - 6 | = 0$

Step 1.2.2

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

x - 6 = \pm 0

$x - 6 = \pm 0$

Step 1.2.3

Plus or minus

0

$0$ is

0

$0$ .

x - 6 = 0

$x - 6 = 0$

Step 1.2.4

Add

6

$6$ to both sides of the equation.

x = 6

$x = 6$

Step 1.2.5

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

x - 6 = \pm 0

$x - 6 = \pm 0$

Step 1.2.6

Plus or minus

0

$0$ is

0

$0$ .

x - 6 = 0

$x - 6 = 0$

Step 1.2.7

Add

6

$6$ to both sides of the equation.

x = 6

$x = 6$

x = 6

$x = 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

(6, 0)

$(6, 0)$

x-intercept(s):

(6, 0)

$(6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = | (0) - 6 |

$y = | (0) - 6 |$

Step 2.2

Simplify

| (0) - 6 |

$| (0) - 6 |$ .

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Step 2.2.1

Subtract

6

$6$ from

0

$0$ .

y = | - 6 |

$y = | - 6 |$

Step 2.2.2

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

- 6

$- 6$ and

0

$0$ is

6

$6$ .

y = 6

$y = 6$

y = 6

$y = 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 6)

$(0, 6)$

y-intercept(s):

(0, 6)

$(0, 6)$

Step 3

List the intersections.

x-intercept(s):

(6, 0)

$(6, 0)$

y-intercept(s):

(0, 6)

$(0, 6)$

Step 4

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

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