y=|x|-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}

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

The final answer is -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

The final answer is -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

The final answer is -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