Graph f(x)=|x-h|+k

$f (x) = | x - h | + k$

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

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

$x - h = 0$

Add $h$ to both sides of the equation.

$x = h$

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

$y = | (h) - h | + k$

Simplify $| (h) - h | + k$ .

Subtract $h$ from $h$ .

$y = | 0 | + k$

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

$y = 0 + k$

Add $0$ and $k$ .

$y = k$

The absolute value vertex is $(h, k)$ .

$(h, k)$

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:

${x | x \in ℝ}$

The absolute value can be graphed using the points around the vertex $(h, k),$

$\begin{array}{c} x & y \\ h & k \end{array}$

Graph f(x)=|x-h|+k

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