Question

Graph –3x^2 + 12y^2 = 84. What are the domain and range?
SOMEONE PLEASE HELP ME !!!!!!!
(PICTURE BELOW)

Answer 1

you have a hyperbola
maybe easier to see if you divide by \(84\)

Answer 2

divide everything by 84 ?

Answer 3

yeah that will put it in standard form for a hyperbola

Answer 4

There all decimals

Answer 5

lol, i mean divide and get
\[\frac{y^2}{7}-\frac{x^2}{28}=1\]

Answer 6

this will help solve the problem
since the \(y^2\) term comes first you know the hyperbola looks like one of the top two choices

Answer 7

12^2/7=decimal

Answer 8

yeah you can write any fraction as some kind of decimal, but that is usually a bad idea
in any case since you have
\[\frac{y^2}{7}-\frac{x^2}{28}=1\]
which looks like
\[\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\] you know it is a hyperbola, so the answer is one of the first two.
and since \(a^2=7\) get get \(a=\sqrt7\) which tells you the range is \(y\leq -\sqrt7\) or \(y\geq \sqrt7\)

Answer 9

Ohh okay i see what your saying. So it has to be between A & B correct.

Answer 10

yes, and the pictures there are identical, so pick the one that says the domain is all real numbers and the range is \(y\leq -\sqrt7\) or \(y\geq \sqrt7\)

Answer 11

Okay i see it. My answer will be A. because A has domain are real number while B says range are all real numbers.

Answer 12

yeah, pick A

Answer 13

Thank you :)

Answer 14

yw