# Thread: State domain and range in set builder notation, plz.

1. ## State domain and range in set builder notation, plz.

State the domain and the range in set builder notation and interval notation. Domain and Range must be written in correct form.

y=-3x-3

Interval Notation:
Domain =
Range =

Set Builder Notation:
Domain =
Domain =

f(x)=-7+|x|

Interval Notation:
Domain =
Range =

Set Builder Notation:
Domain =
Domain =

2. Originally Posted by Insignia21

State the domain and the range in set builder notation and interval notation. Domain and Range must be written in correct form.

y=-3x-3

Interval Notation:
Domain =
Range =

Set Builder Notation:
Domain =
Domain =

f(x)=-7+|x|

Interval Notation:
Domain =
Range =

Set Builder Notation:
Domain =
Domain =
Unless otherwise stated, polynomial functions and absolute value functions have a domain of $\mathbf{R}$. In other words, you can let $x$ take on any value you like.

In interval notation, this domain is $(-\infty, \infty)$.

For the function $y = -3x - 3$, this is a linear function, which is a straight line infinitely long in both directions. So the range is also $\mathbf{R}$, or $(-\infty, \infty)$.

For the function $y = -7 + |x|$, we first need to consider the $|x|$.

The absolute value function "gobbles up" all negatives and turns them positive. Thus the range of $|x|$ is $x \geq 0$ or $[0, \infty)$.

Subtracting 7 gives a vertical translation of 7 units down.

So the range of $y = -7 + |x|$ is $x \geq -7$ or $[-7, \infty)$.