Question

Graphing square root functions, how do you know if the equation will be less than or equal to, or greater than or equal to?

Answer 1

can you give an example of what you mean? im not sure I understand your'e question

Answer 2

\[y=4/7\sqrt{18-x}\] I am trying to find the domain of this function. I know I use teh square toot part, btu Im not sure how to find out if it would be greater than or equal to, or less than or equal to.

Answer 3

ok. i got you

Answer 4

so, when we write the square root symbol, we are only asking for what are known as real numbers. there is something called "imaginary numbers." I know it sounds like im making this up but im not. we get imaginary number when we try to take the square root of a negative number.

Answer 5

because these numbers aren't real we try to only take the square root of positive numbers (including zero)

Answer 6

Ok, I understand that.

Answer 7

so, the first thing we need to is make sure the number under the square root is not negative.

Answer 8

have you ever heard the term "undefined"?

Answer 9

Yes.

Answer 10

is that sqrt in the denominator as well?

Answer 11

No the square root isnt, teh equation is a fraction and a sqaure root but they are separate.

Answer 12

so when something is undefined it means that the math just doesn't make sense. one of most common examples of undefined things is when you have 0 as a denominator

Answer 13

just making sure :) if it was under, then sqrt(0) would have to be weeded out as well

Answer 14

exactly

Answer 15

as a rule of thumb for "real" solutions; we have a few rules, no dividing by zero, no negative sqrts, and keep you logs positive

Answer 16

well, no negative even roots, sqrt is even since it implies a 2

Answer 17

Ok, I see how all of that works. But Im still confused about how to find the domain of a square root function.

Answer 18

so for this domain (all valid x values) we want the sqrt arguement (18-x) to be greater than or equal to zero.; therefore you would just need to solve:\[18-x \ge0\]

Answer 19

add x to both sides, what do you end up with?

Answer 20

\[18\ge x\]

Answer 21

good, and notice that since "x" is on the smaller end of the ">", we read it as; x is smaller than or equal to 18

Answer 22

Ok, that makes sense. Thank you :)

Answer 23

youre welcome, and good luck :)