Question

Finding X in a Vertical Asymptote?

Answer 1

I'm confused, honestly. I've tried Google and looking through my textbook again and again, but it's neglecting to help me.

The problem I have is Y = 5/x + 2, alright? I find the excluded value, which would be -2. Now, continuing in the lesson, they tell me to graph the function and continue with the example. "Use values of 'x' near -2," they tell me.

... Then, they show me this table:

x|-7|-4|-3|-1|0|3
y|5/-7+2|... and that continues with plugged in numbers.

My question is how they got the 'x'. (-7. -4, -3, -1, 0, 3)


Is there an equation I have to follow, do I pick the numbers at random, are there certain rules I must follow while picking numbers, ect?

I appreciate all help, so thank you in advance!

Answer 2

They just chose numbers at random.

Answer 3

My confusion still lies. I had another problem directly after the sample problem,

"h(x) = -3/x-6" Using the excluded value method again, I determined my number would be 6.

So, then I continued on with that and had a table ready to graph... when I graphed, it didn't look quite like an asymptote graph should. The numbers I used were, -7, -5. -3. -1, 1 and 9. Did I do something wrong?

Answer 4

You want to use a range of numbers that has the asymptote in the middle to have a better view (even better with smaller numbers).

Using your problem as an example, I know that the asymptote is going to be 6. Using their scale of +/- 5, I would use a range of:
(1, 3 , 5, 7, 9, 11)
As you can see, the lowest and highest numbers are +/- 5 away from the asympote. I used increments of 2 because I felt that it was the most reasonable. You can use whatever range of numbers you want, with however many numbers you want. Just make sure your asympote is in the middle of your list of test points.

If you want even better results, use numbers a few decimals away from the number.
So, going back to the example, a scale that uses decimals would be like:
(5.9, 5.99, 5.999, 6.001, 6.01, 6.1)
With this interval, you can more clearly see that the equation is going towards negative infinity as it approaches the asympote.

Answer 5

That actually helps a lot, thanks! I understand a lot better now. In the future, I'll probable keep to a scale of +/- five to figure out answers.

Answer 6

probably*

Answer 7

+/- 5 was based off the example you gave me. Assuming you're not in calculus, you want to prepare for higher levels (such as calculus) by using smaller scales.