Question

For x ≥ 0, the line y=2 is an asymptote for the graph of the function f, Which of the following statements must be true?
(a) f(0)=2
(b) f(x)≠2 for all x≥0
(c) f(2) is undefined
(d) lim x->2 f(x)=∞
(e) lim x->∞ f(x)=2

Answer 1

that was what I had answered on my test and I had gotten it wrong

Answer 2

wow really?

Answer 3

yeah...

Answer 4

then the statements are misleading
i am not yet familiar with lim statements so don't know how to interpret d and e

Answer 5

i hop someone comes and explains, i'd like to know too

Answer 6

thanks for trying :)

Answer 7

help? someone? anyone? if you're not too busy? @shamil98 @Hero

Answer 8

could you help me if you're not too busy please? @hartnn

Answer 9

Correct choice is (E) by definition of a horizontal asymptote.

Answer 10

thanks :)

Answer 11

To find the horizontal asymptote of a function, take the limit of the function as x approaches infinity. If the limit is a number L, then L is its horizontal asymptote.

Answer 12

If lim (x-->infinity) f(x) = a, then f(x) has horizontal asymptote y=a. Since y=2 is a horizontal asymptote, this limit must equal 2, so E is true.

Also, since y=2 is an asymptote, f(x) cannot equal 2 for x>=0, so B is also true.

Answer 13

I had gotten the question wrong on my test for answering b

Answer 14

B is false, a curve can pass through its asymptote.

Answer 15

ohhh right, thanks so much! :D

Answer 16

Some students think that a curbe can never pass through its asymptote, but that is absolutely false. In class, I am sure your professor has given you examples of such functions.

Answer 17

I had failed the marking period that had that stuff, but I kinda understand :) thanks <3