# Graph f(x)=|x+2|

f(x)=|x+2|
Find the absolute value vertex. In this case, the vertex for y=|x+2| is (-2,0).
To find the x coordinate of the vertex, set the inside of the absolute value x+2 equal to 0. In this case, x+2=0.
x+2=0
Subtract 2 from both sides of the equation.
x=-2
Replace the variable x with -2 in the expression.
y=|(-2)+2|
Simplify |(-2)+2|.
y=|0|
The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.
y=0
y=0
The absolute value vertex is (-2,0).
(-2,0)
(-2,0)
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:
(-∞,∞)
Set-Builder Notation:
{x|x∈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.
Substitute the x value -4 into f(x)=|x+2|. In this case, the point is (-4,2).
Replace the variable x with -4 in the expression.
f(-4)=|(-4)+2|
Simplify the result.
f(-4)=|-2|
The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.
f(-4)=2
y=2
y=2
y=2
Substitute the x value -3 into f(x)=|x+2|. In this case, the point is (-3,1).
Replace the variable x with -3 in the expression.
f(-3)=|(-3)+2|
Simplify the result.
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
y=1
y=1
y=1
Substitute the x value 0 into f(x)=|x+2|. In this case, the point is (0,2).
Replace the variable x with 0 in the expression.
f(0)=|(0)+2|
Simplify the result.
f(0)=|2|
The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.
f(0)=2