For a function p(x) , as |x| → ∞ then p(x) → 2. Which of the following graphs could be p(x)?

- anonymous

For a function p(x) , as |x| → ∞ then p(x) → 2. Which of the following graphs could be p(x)?

- schrodinger

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- anonymous

##### 1 Attachment

- ganeshie8

as \(|x|\to\infty\)
means \(x\to \infty\), \(x\to -\infty\)

- ganeshie8

so we're given that the graph approaches \(2\) as you go left and right extremes on x axis

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## More answers

- anonymous

I wasn't sure what the arrow meant. I searched but got conflicting answers. Most said that it was interchangeable with the equals sign though. Is this correct?

- ganeshie8

good question,
\(\to\) is read as "tends to" or "approaches"

- anonymous

Okay, I think I got it, @ganeshie8.
If I am right, the answer should be graph D, correct?
Or am I way off?

- ganeshie8

Is the function approaching "2" as you walk right or left extremes on x axis ?
|dw:1435298726902:dw|

- anonymous

I don't think I have a great understanding on what extremes are, because I did think the function was approaching 2..

- anonymous

- ganeshie8

whats the approximate value of function in graph D at x=10 ?

- anonymous

Oh! approx. 1.2ish, not 2

- ganeshie8

can you guess the apprximate value at x=1000000 ?

- ganeshie8

it seems the graph is approaching x axis yes ?

- anonymous

so it's like an asymptote; always getting near the x-axis, but not quite touching it?

- anonymous

the value at 1000000 would be very minimal.

- ganeshie8

yes it is almost 0, and the more extreme right you go, the more closer the function approaches 0

- anonymous

okay..

- anonymous

so then that narrows it down to A and B

- anonymous

No, just B

- ganeshie8

In B, what does the graph approach to as you go extreme right ?

- anonymous

Oh it is increasing

- ganeshie8

|dw:1435301616932:dw|

- ganeshie8

looks the graph is approaching "4" as you go extreme right yes ?

- anonymous

I just looked at what was closer to it, distance wise near the beginning of the curve. It would get farther away from 2 as you go more extreme right

- anonymous

yes

- ganeshie8

look at option C

- anonymous

Oh, and even A is curving slightly upwards.

- ganeshie8

|dw:1435301725529:dw|

- anonymous

Wow. Thanks for tolerating me, this must have been frustrating.
I'll write a testimonial for your troubles

- ganeshie8

glad you figured out the answer finally! but trust me, it is not frustrating at all when somebody engages with you completely, asks relevant questions and tries hard to understand the concept.

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