f(x)=|x+2|

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|.

Add -2 and 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}

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.

Add -4 and 2.

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

The final answer is 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.

Add -3 and 2.

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

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.

Add 0 and 2.

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

The final answer is 2.

y=2

y=2

y=2

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

xy-42-31-20-1102

xy-42-31-20-1102

Graph f(x)=|x+2|