y=3|X|-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}

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

The final answer is 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

The final answer is -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

The final answer is 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