C1, Asymtope question

Question: http://imgur.com/a/9VUWv
Answer: http://imgur.com/a/iqfLH

The question in I'm confused about is 11 B. I had no problem answering the rest.

Does the question mean where the asymtope cross the Y axis?

Is the answer y = 4 and x = 0, or (0, 4)?

(edited 6 years ago)

Original post by mojos

Question: http://imgur.com/a/9VUWv
Answer: http://imgur.com/a/iqfLH

The question in I'm confused about is 11 B. I had no problem answering the rest.

Does the question mean where the asymtope cross the Y axis?

Is the answer y = 4 and x = 0, or (0, 4)?

No it's asking for the equations of the asymptotes, not a pair of coordinates. For example, take the line

x=0

which is an asymptote, and you notice that the graph approaches this line as

y\rightarrow \pm \infty

You understand what an asymptote is, yes?

(edited 6 years ago)

Reply 2

mojos

OP

5

Just re read the text book I get it now.

The asymptote are the lines that the curves approach very closely but do not touch. There are two, the vertical and horizontal.

For the question above, the horizontal line is x = 0, and the vertical is y = 4.

This is because equation can be shown as f(x) = (3/x), f(x) + 4. Which means the whole graph has been lifted upwards by 4.

Original post by mojos

Just re read the text book I get it now.

The asymptote are the lines that the curves approach very closely but do not touch. There are two, the vertical and horizontal.

For the question above, the horizontal line is x = 0, and the vertical is y = 4.

This is because equation can be shown as f(x) = (3/x), f(x) + 4. Which means the whole graph has been lifted upwards by 4.

Yes. Technically an asymptote is some function that your function approaches. Your function CAN cross the asymptote function, and there ARE asymptotes other than the vertical and horizontal ones, but for C1 you only need to be aware of these simple vertical/horizontal ones.

Another way it can be shown is that what happens to

\frac{3}{x}+4

when

x \rightarrow \infty

?? Well x is on the denominator and as the denominator grows, the fraction overall gets smaller and smaller so it tends to 0. So the limit of it is 0, thus the limit of