# Graph y=|x|-9 y=|x|-9
Find the absolute value vertex. In this case, the vertex for y=|x|-9 is (0,-9).
To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case, x=0.
x=0
Replace the variable x with 0 in the expression.
y=|0|-9
Simplify |0|-9.
The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.
y=0-9
Subtract 9 from 0.
y=-9
y=-9
The absolute value vertex is (0,-9).
(0,-9)
(0,-9)
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 -2 into f(x)=|x|-9. In this case, the point is (-2,-7).
Replace the variable x with -2 in the expression.
f(-2)=|-2|-9
Simplify the result.
The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.
f(-2)=2-9
Subtract 9 from 2.
f(-2)=-7
y=-7
y=-7
y=-7
Substitute the x value -1 into f(x)=|x|-9. In this case, the point is (-1,-8).
Replace the variable x with -1 in the expression.
f(-1)=|-1|-9
Simplify the result.
The absolute value is the distance between a number and zero. The distance between -1 and 0 is 1.
f(-1)=1-9
Subtract 9 from 1.
f(-1)=-8
y=-8
y=-8
y=-8
Substitute the x value 2 into f(x)=|x|-9. In this case, the point is (2,-7).
Replace the variable x with 2 in the expression.
f(2)=|2|-9
Simplify the result.
The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.
f(2)=2-9
Subtract 9 from 2.
f(2)=-7
y=-7
y=-7
y=-7
The absolute value can be graphed using the points around the vertex (0,-9),(-2,-7),(-1,-8),(1,-8),(2,-7)
xy-2-7-1-80-91-82-7
xy-2-7-1-80-91-82-7
Graph y=|x|-9     