Question

what is the range of the function y = 6/(X - 12)?
thanks.

Answer 1

Do you know what range is?

Answer 2

yes, we consider teh values of y.

Answer 3

will we multiply both sides by x - 12 first?

Answer 4

In this example, we don't need to.

Answer 5

And you generally don't need to do so as this is a y=f(x), so keep the left hand side as simple as possible.

Answer 6

can we do x = 6/y + 12? so, range is (-ing, 0)U(0, inf)?

Answer 7

which is the same with \[y\in(-\infty,\infty)\]

Answer 8

you mean, we can include y = 0?

Answer 9

Yes, when x tends to plus or minus infinity.

Answer 10

But please be minded that if we are using real analysis, the range will instead read \[y\in (\infty,0)\cup(0,\infty)\]

Answer 11

i am confused sorry..

Answer 12

If you use limit, you find that y can be zero if x hypothetically reach infinity.

But in reality you can't, so most people will instead exclude zero.

Answer 13

oh okay, but, if you were asked to write it in interval notation, how will you write it?

Answer 14

Yours is find enough.

Answer 15

As you did earlier, \[ (-\inf, 0) \cup (0, \inf)\] is interval notation.

Answer 16

oh okay.. thanks..

Answer 17

it's easier to see it as x=6/y + 12

Answer 18

as you can see the only value y can't be is 0.

Answer 19

the range of this function is 0 to - infinity

Answer 20

there is a horizontal asymptote at y = 0

Answer 21

@campbell_st you forgot 0 to +infinity...