Help with the Functions Unit

[Dax]

Hi Guys, I needed some help with the Functions Unit, especially graphing functions without a calculator and finding their reflects in y = x or their inverse etc.

I usually have problems in functions that involve an Asymptot or turns into an asymtot when you graph their inverse etc.

Any suggestions on how to tackle these kinds of problems? Also, any tutorials both visual and text based will be really appreciated.

Thanks!

[twilight]

Can you be more specific with your question? Like give an example of a question.

Asymptotic behaviour is determined using limits, which is not heavily focused in the IB syllabus (at least not in the old one). But the asymptotes they usually ask you to find are quite easy, you don't necessarily need to compute the limits.

For horizontal asymptote, you take the limit as x approaches positive and negative infinity and the value you get is your asymptote.

For the vertical asymptotes, it's just wherever where the denominator cannot be 0.

Are you talking about inverse function or reciprocal function?

[Dax]

May 11. 1Z2. 05

May 10. 1Z1. 05 Part b

Nov 10. 2. 08

These are examples of types of questions that I have doubts in. Generally graphing from a already given graph and things like that give me some doubts

Edited March 21, 2014 by Dax

[twilight]

For M11 TZ2,

1. Everywhere where y=0 on the y=f(x) graph, when you take the reciprocal, it becomes 1/0 which approaches infinity, so at x=0 and x=2, you have vertical asymptotes.

2. On the y=f(x) graph, there is horizontal asymptote at y=2. When you take the reciprocal, the horizontal asymptote becomes 1/2. On the y=f(x) graph, y approaches 2 as x approaches negative infinity. Therefore, when you take the reciprocal, y will approach 1/2 as x approaches negative infinity. As x approaches positive infinity 1/y will approach 0.

I suppose you know how to get the other parts, like minimum becomes maximum etc.

For 5b, you have to do it 'manually'. So you first find the points which are easy to find, which are basically at x=0 and x=2 because you know that when x=0, f(x)=0, so y=0. At x=2, f(2)=0, so y=0. To find how the graph looks like on the other parts, substitute values. Let's say in the original graph when x=1, f(1)=-1. You don't know that this is the case, but it doesn't matter because you just need the shape of the graph. And then you see what happens when x=-2 or any other negative number, it doesn't matter, and also when x=3 or any other positive number.

For M10 TZ1,

1. Find the vertical asymptotes for the reciprocal graph. You see on the original graph that x=-2 is a vertical asymptote. But with the reciprocal graph, you know x=-2 gives you a valid solution.

2. Find the horizontal asymptote.

Since it's a modulus function, just reflect the part below the x-axis to the positive side.

For N10,

You need to do this manually, similar to the M11 question.

So you first find the 'critical' points (this is what I call them) where f(x)=0 and g(x)=0. When f(x)=0, you know the f/g will be 0. When g(x)=0, f/0 will be undefined so you know that will be a vertical asymptote.

When f(x)=g(x), f/g will be 1. And then you find the remaining points by substituting certain values, and then you can sketch the graph from there.

Sorry if this is not clear, I'm not exactly sure how much you know/ don't know. Feel free to ask if there's some more you're not clear about.

[Dax]

Thanks a lot, I'm quite okay with this topic now. Thanks a lot for the explanation. It really is quite well written and descriptive!