Graph f(x)=|x-4| - MathMaster

$f (x) = | x - 4 |$

Find the absolute value vertex. In this case, the vertex for $y = | x - 4 |$ is $(4, 0)$ .

Tap for more steps…

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 4$ equal to $0$ . In this case, $x - 4 = 0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Replace the variable $x$ with $4$ in the expression.

$y = | (4) - 4 |$

Simplify $| (4) - 4 |$ .

Tap for more steps…

Subtract $4$ from $4$ .

$y = | 0 |$

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 $(4, 0)$ .

$(4, 0)$

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:

${x | x \in ℝ}$

For each $x$ value, there is one $y$ value. Select 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.

Tap for more steps…

Substitute the $x$ value $2$ into $f (x) = | x - 4 |$ . In this case, the point is $(2, 2)$ .

Tap for more steps…

Replace the variable $x$ with $2$ in the expression.

$f (2) = | (2) - 4 |$

Simplify the result.

Tap for more steps…

Subtract $4$ from $2$ .

$f (2) = | - 2 |$

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

$f (2) = 2$

The final answer is $2$ .

$y = 2$

Substitute the $x$ value $3$ into $f (x) = | x - 4 |$ . In this case, the point is $(3, 1)$ .

Tap for more steps…

Replace the variable $x$ with $3$ in the expression.

$f (3) = | (3) - 4 |$

Simplify the result.

Tap for more steps…

Subtract $4$ from $3$ .

$f (3) = | - 1 |$

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

$f (3) = 1$

The final answer is $1$ .

$y = 1$

Substitute the $x$ value $6$ into $f (x) = | x - 4 |$ . In this case, the point is $(6, 2)$ .

Tap for more steps…

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

$f (6) = | (6) - 4 |$

Simplify the result.

Tap for more steps…

Subtract $4$ from $6$ .

$f (6) = | 2 |$

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

$f (6) = 2$

The final answer is $2$ .

$y = 2$

The absolute value can be graphed using the points around the vertex $(4, 0), (2, 2), (3, 1), (5, 1), (6, 2)$

$\begin{array}{c} x & y \\ 2 & 2 \\ 3 & 1 \\ 4 & 0 \\ 5 & 1 \\ 6 & 2 \end{array}$

Graph f(x)=|x-4|

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store