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**Jacobpm****Guest**

For f(x) = (2x + 5) / |3x - 4|, use graphs and tables to find the limit as x approaches infinity of f(x) and the limit as x approaches negative infinity of f(x)... Also identify any horizontal asymptotes...

When i graph the function in my graphing calculator, it looks like y will never reach a specific value as x approaches pos or neg infinity.. i went to table and checked at x value or 20000000 and -200000000 and i get 2/3 and -2/3 respectively

is this correct?

limit as x approaches pos inf = 2/3

limit as x approaches neg inf = -2/3

I'm not sure about the horizontal asymptotes?

would they be y = 2/3 and y = -2/3? I think? or is it something in between that?

Thanks for the input.

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Horizontal asymptotes are the limits as x approaches infinity.

If

where c is a constant, then the horizontal asymptote is x = c. Same applies for negative infinity.You're answers are correct. Whenever you have a polynomial division, where a*x^n and b*x^n are the highest terms for each the numerator and the denominator, than a horizontal asymptote exists at a/b. Note that both n's have to be the same. In other words, this does not apply to 5x^3 / 2x^2.

Edited to add:

if you have a*x^n and b*x^m as the highest terms in the polynomial division, then:

if n > m, the function goes to infinity

if n < m, the function has a horizontal asymptote at x = 0

if n = m, the function has a horizontal asymptote at a/b

*Last edited by Ricky (2006-01-02 11:22:36)*

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

If x->+oo the function f is:

f(x)=(2x+5)/(3x-4). We'll find the limit:

*Last edited by krassi_holmz (2006-01-02 11:30:05)*

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Analogic,

2

lim f(x) = - ---

x--> -oo 3

IPBLE: Increasing Performance By Lowering Expectations.

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