y=|x+3|-3

To find the x coordinate of the vertex, set the inside of the absolute value x+3 equal to 0. In this case, x+3=0.

x+3=0

Subtract 3 from both sides of the equation.

x=-3

Replace the variable x with -3 in the expression.

y=|(-3)+3|-3

Simplify |(-3)+3|-3.

Simplify each term.

Add -3 and 3.

y=|0|-3

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

y=0-3

y=0-3

Subtract 3 from 0.

y=-3

y=-3

The absolute value vertex is (-3,-3).

(-3,-3)

(-3,-3)

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 -5 into f(x)=|x+3|-3. In this case, the point is (-5,-1).

Replace the variable x with -5 in the expression.

f(-5)=|(-5)+3|-3

Simplify the result.

Simplify each term.

Add -5 and 3.

f(-5)=|-2|-3

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

f(-5)=2-3

f(-5)=2-3

Subtract 3 from 2.

f(-5)=-1

The final answer is -1.

y=-1

y=-1

y=-1

Substitute the x value -4 into f(x)=|x+3|-3. In this case, the point is (-4,-2).

Replace the variable x with -4 in the expression.

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

Simplify the result.

Simplify each term.

Add -4 and 3.

f(-4)=|-1|-3

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

f(-4)=1-3

f(-4)=1-3

Subtract 3 from 1.

f(-4)=-2

The final answer is -2.

y=-2

y=-2

y=-2

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

Replace the variable x with -1 in the expression.

f(-1)=|(-1)+3|-3

Simplify the result.

Simplify each term.

Add -1 and 3.

f(-1)=|2|-3

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

f(-1)=2-3

f(-1)=2-3

Subtract 3 from 2.

f(-1)=-1

The final answer is -1.

y=-1

y=-1

y=-1

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

xy-5-1-4-2-3-3-2-2-1-1

xy-5-1-4-2-3-3-2-2-1-1

Graph y=|x+3|-3