Question

I now just need help finding the upper range of the below equation. I have the domain as (-3,3) and the range [2/(sqrrt(3), ?????] thanks for the help!!

Please help me find the domain and range of :
y=2/(4th root(9-x^2)

Answer 1

Domain is first number and range would be the second number. so just find the x and y

Answer 2

which part are you stuck at

Answer 3

having even roots in a problem
you will have some restrictions if the thing inside is less than 0
also having fractions can be a problem because we don't want to divide by 0
you need to make sure the thing inside your 4th root there is positive

Answer 4

so is the domain -3 to 3?

Answer 5

but not including 3?

Answer 6

sounds good not including either -3 or 3

Answer 7

so then do you put -3 and 3 into the equation to get the range limits?

Answer 8

but then that would give you zeros for the denominator so what then?

Answer 9

what happens when you take 1 and divide it by numbers that get really really close to 0?

Answer 10

like what is 1/.00001 equal to?
is that actually a big number?

Answer 11

yeah infinity

Answer 12

and we restricted our domain so that the function exists over the real numbers
we basically have a positive divided by a positive so we know that are range will exist only for positive numbers and it actually goes to infinity
but we also need to figure out the lowest y value

Answer 13

the thing will be the smallest if you replace x with 0 and solve for y

Answer 14

that would be 2/(4th rt(9) - our teacher makes us do specific answers, no decimals

Answer 15

so that is the low end of our range

Answer 16

you could simplify that though

Answer 17

so the top end would be when x is close to 3 but not 3?

Answer 18

\[\sqrt[4]{9}=\sqrt[4]{3^2}=3^\frac{2}{4}=?\]

Answer 19

sorry my computer kicked me off

Answer 20

I am not sure, I see how you got to that point though

Answer 21

oh duh, are you just saying 3^1/2?

Answer 22

so 2/sqrt(3)?

Answer 23

well yeah that would be the smallest of the range

Answer 24

and then you noticed that if you plug in either endpoint the bottom was getting closer to zero therefore the fraction was getting positive large

Answer 25

so do you what the range is?

Answer 26

also you weren't the only one having problems
i couldn't get openstudy to load for like 5 to 6 minutes

Answer 27

Any help on the upper part of the range? I get that x=0 at the low end, and x should = 3 at the upper end, but 3 cannot be included, so it is a number infanetly close to three and i can't wrap my brain around that?

Answer 28

emily we already got the upper part

Answer 29

and the domain doesn't include -3 or 3, but would the range include both numbers? I feel like it should include them?

Answer 30

remember you said the the function was getting huge as our x's approaches x=3 or x=-3

Answer 31

the domain is (-3,3)

Answer 32

the range is [2/sqrt(3),inf)
because the smallest was 2/sqrt(3)
and because the function got huge when the bottom went to 0

Answer 33

got positive huge*

Answer 34

emily do you understand?

Answer 35

Oh wow, yeah duh, it would be infinity wouldnt it? Thanks!