# Graph y=3|X|-4 y=3|X|-4
Find the absolute value vertex. In this case, the vertex for y=3|x|-4 is (0,-4).
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=3|0|-4
Simplify 3|0|-4.
Simplify each term.
The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.
y=3⋅0-4
Multiply 3 by 0.
y=0-4
y=0-4
Subtract 4 from 0.
y=-4
y=-4
The absolute value vertex is (0,-4).
(0,-4)
(0,-4)
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)=3|x|-4. In this case, the point is (-2,2).
Replace the variable x with -2 in the expression.
f(-2)=3|-2|-4
Simplify the result.
Simplify each term.
The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.
f(-2)=3⋅2-4
Multiply 3 by 2.
f(-2)=6-4
f(-2)=6-4
Subtract 4 from 6.
f(-2)=2
y=2
y=2
y=2
Substitute the x value -1 into f(x)=3|x|-4. In this case, the point is (-1,-1).
Replace the variable x with -1 in the expression.
f(-1)=3|-1|-4
Simplify the result.
Simplify each term.
The absolute value is the distance between a number and zero. The distance between -1 and 0 is 1.
f(-1)=3⋅1-4
Multiply 3 by 1.
f(-1)=3-4
f(-1)=3-4
Subtract 4 from 3.
f(-1)=-1
y=-1
y=-1
y=-1
Substitute the x value 2 into f(x)=3|x|-4. In this case, the point is (2,2).
Replace the variable x with 2 in the expression.
f(2)=3|2|-4
Simplify the result.
Simplify each term.
The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.
f(2)=3⋅2-4
Multiply 3 by 2.
f(2)=6-4
f(2)=6-4
Subtract 4 from 6.
f(2)=2
y=2
y=2
y=2
The absolute value can be graphed using the points around the vertex (0,-4),(-2,2),(-1,-1),(1,-1),(2,2)
xy-22-1-10-41-122
xy-22-1-10-41-122
Graph y=3|X|-4     