Question

domain and range of square root of x+6

Answer 1

Is it

\[\Large \sqrt{x+6}\]

or is it

\[\Large \sqrt{x}+6\]

??

Also, how far did you get with this problem?

Answer 2

1st one. I figured x=/= -6, but i'm not sure if the domain and range would be unions or not.

Answer 3

i got this question and i believe the domain is (-6,infinity) and (0,infinity) i could be wrong though...

Answer 4

well let's see what happens when x = -6

\[\Large \sqrt{x+6}\]

\[\Large \sqrt{-6+6}\]

\[\Large \sqrt{0}\]

\[\Large 0\]

So x = -6 is certainly possible and allowed in the domain.

Answer 5

oh, because it has to be either 0 or a positive number?

Answer 6

It turns out that the radicand (basically the stuff under the square root) cannot be negative.

So...

\[\Large x + 6 \ge 0\]

\[\Large x + 6{\color{red}-6} \ge 0{\color{red}-6}\]

\[\Large x + 0 \ge -6\]

\[\Large x \ge -6\]

Answer 7

the radicand, yes, it must be 0 or positive

Answer 8

so, the range is x is greater than or equal to -6? How would I figure out the range?

Answer 9

What's the smallest value in the domain?

Answer 10

-6?

Answer 11

plug that into the function to get ???

Answer 12

ohh! square root of 0?

Answer 13

which is ???

Answer 14

0

Answer 15

So that's the smallest value in the range.

Smallest value in domain ----> smallest value in the range

Answer 16

This only works because the function sqrt(x+6) is always increasing.

Answer 17

I get it, thank you :P

Answer 18

you're welcome