Question

write an equation for the translation of y=6/x that has the asymptotes x=4 and y=5

Answer 1

and this one: What are the points of discontinuity? y=x-2/x^2+5x-6

Answer 2

Do you know where the asymptotes are for this function?
\[\Large\rm y=\frac{6}{x}\]
What? At y=0 and x=0 you say? Ah yes very good!
Lemme show you how I like to deal with this type of problem.
It might not be how your teacher explained it, but it's worth checking out at least. :)

To shift to our asymptotes, we `subtract` the new value from our x or y.
So to shift our asymptote 4 to the `right` (moving it to x=4),
we subtract 4 from x.\[\Large\rm y=\frac{6}{x-4}\]Then to shift it `up` 5 (moving it to y=5),
we subtract 5 from y,\[\Large\rm y-5=\frac{6}{x-4}\]But they will want this in the form y=
so we need to add 5 to each side to get it into that form.

Answer 3

Thankyou so much :)

Answer 4

Would it be Y= 6/x-4+5?

Answer 5

Yes, but be careful the way you write that in text!
I think what you meant to write was,

y=6/(x-4)+5 <- this shows that both the x and 4 are in the denominator.

Answer 6

`What are the points of discontinuity?`\[\Large\rm y=\frac{x-2}{x^2+5x-6}\]

Answer 7

To do this one, you need to start by `factoring` the denominator.
Understand how to do that?

Answer 8

No. :(

Answer 9

\[\Large\rm x^2+5x-6\]So you need two numbers that:
`multiply to -6`
`add to 5`

Let's try ummm,\[\Large\rm -2\cdot3=-6\]\[\Large\rm \color{red}{-2+3\ne5}\]Mmmm -2 and 3 didn't work out :(
Can you think of any other factors of -6?

Answer 10

-3? 1?

Answer 11

\[\Large\rm \color{red}{-3\cdot1\ne -6}\]Hmm nope those are not factors of -6 :[