Question

whats are the horizontal and vertical asymptotes for y=3^x+3 ?

Answer 1

Do you mean \(y = 3^{x} + 3\), as you have written it? Or, did you mean something else?

Answer 2

its as i've written it, just like in my book

Answer 3

the exponent is x+3

Answer 4

Then it is NOT as you have written it. You should have written y = 3^(x+3). This is the same as \(y = 3^{x+3}\). Do you see the difference it makes when adding the parentheses? You must remember your Order of Operations.

Answer 5

yes, i see that. thank you. sorry

Answer 6

No worries. Writing in-line is very different from formatted printing in a book. Think very hard on your Order of Operations. Make sure you write what you mean.

\(y = 3^{x+3}\)

What is the LEAST value that can be obtained for y? Can you find a value for x that gives y = 1? How about a value for x that gives y = 0?

Answer 7

x has to =0 to get y=1

Answer 8

Okay, we managed y = 1. How about y = 0? Can we do that?

Answer 9

cant get it

Answer 10

the answer says that y>0. but i cant see how they get that

Answer 11

How close can you get?

\(y = 3^{-3+3} = 3^{0} = 1\) -- We got that, already.

\(y = 3^{-4+3} = 3^{-1} = 1/3\)

\(y = 3^{-5+3} = 3^{-2} = 1/9\)

\(y = 3^{-6+3} = 3^{-3} = 1/27\)

Do you see where this is going? Will it EVER get negative? How close to zero can we make it?

Answer 12

oh. so the restriction is to always use positive values. otherwise we cant get anywhere. thank you so much!

Answer 13

Not USE positive values for y, but observe that you can't GET a negative value for y. You can snuggle up to y = 0, as close as you like, but you can't quite get there!

Answer 14

yeah, i see that now. thanks :)