# Graph y=|x+3|-3 y=|x+3|-3
Find the absolute value vertex. In this case, the vertex for y=|x+3|-3 is (-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.
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}
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 -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.
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
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.
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
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.
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
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     