Question

I was able to solve five problems by myself but I need help with this one: Describe the properties of the graph below. Your description should include function values as well as limits at all points of discontinuity on the graph.

Answer 1

So how far can you get on your own with this one?

Answer 2

So first I was going to do the limit as x approaches 1

Answer 3

Is that something I should do?

Answer 4

How do I describe the properties?

Answer 5

I'm not taking the class, so I'm not entirely sure what your professor expects but I'd definitely say:

What's that red line?
What's the limit as x approaches 1 from the left, the right, and from both sides at the same time?
What's the value of f(x) at x=1?

Answer 6

You can even talk about concavity and the range and domain of the graph if your professor wants it. I'm sure there are other things too.

Answer 7

What is the red line?

Answer 8

Is that the asymptote?

Answer 9

The function has discontinuity at x = 0.

You need to find f(0), and the left and right limits at x = 0.

Answer 10

Okay that is what I am going to do. Thanks everyone!

Answer 11

You are welcome.

And since they are asking for property of the function, in addition to the above, also state that the function has a horizontal asymptote at y = 2 (that is when x-> -infinity)

Answer 12

not at y = 2 but horizontal asymptote y = 2.

Answer 13

awesome. That is what I will do. Thanks everyone!

Answer 14

yw.

Answer 15

Whoops I said x=1 when I meant x=0. Looks like ranga got you all sorted out though, so good! =)

Answer 16

Thanks for helping though @Kainui though. I get those things mixed up all the time.

Answer 17

I became a fan of you.

Answer 18

Alright! :)