Graph y=|x-8|

$y = | x - 8 |$

Step 1

Find the absolute value vertex. In this case, the vertex for $y = | x - 8 |$ is $(8, 0)$ .

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 8$ equal to $0$ . In this case, $x - 8 = 0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Replace the variable $x$ with $8$ in the expression.

$y = | (8) - 8 |$

Simplify $| (8) - 8 |$ .

Subtract $8$ from $8$ .

$y = | 0 |$

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

$y = 0$

The absolute value vertex is $(8, 0)$ .

$(8, 0)$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

For each $x$ value, there is one $y$ value. Select a few $x$ values from the domain. It would be more useful to select the values so that they are around the $x$ value of the absolute value vertex.

Substitute the $x$ value $6$ into $f (x) = | x - 8 |$ . In this case, the point is $(6, 2)$ .

Replace the variable $x$ with $6$ in the expression.

$f (6) = | (6) - 8 |$

Simplify the result.

Subtract $8$ from $6$ .

$f (6) = | - 2 |$

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

$f (6) = 2$

The final answer is $2$ .

$y = 2$

Substitute the $x$ value $7$ into $f (x) = | x - 8 |$ . In this case, the point is $(7, 1)$ .

Replace the variable $x$ with $7$ in the expression.

$f (7) = | (7) - 8 |$

Simplify the result.

Subtract $8$ from $7$ .

$f (7) = | - 1 |$

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

$f (7) = 1$

The final answer is $1$ .

$y = 1$

Substitute the $x$ value $10$ into $f (x) = | x - 8 |$ . In this case, the point is $(10, 2)$ .

Replace the variable $x$ with $10$ in the expression.

$f (10) = | (10) - 8 |$

Simplify the result.

Subtract $8$ from $10$ .

$f (10) = | 2 |$

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

$f (10) = 2$

The final answer is $2$ .

$y = 2$

The absolute value can be graphed using the points around the vertex $(8, 0), (6, 2), (7, 1), (9, 1), (10, 2)$

$\begin{array}{c} x & y \\ 6 & 2 \\ 7 & 1 \\ 8 & 0 \\ 9 & 1 \\ 10 & 2 \end{array}$

Step 4

Graph y=|x-8|

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