I'm taking this math class and I'm suppose to find the vertical, horizontal and oblique asymptote, if any for the following equation...

f(x) = 11 - (5x/5x^2 + 7x - 12)

by NOT, i repeat NOT looking at a graph of the function.

Thanks...

Your school is NOT the subject.

f(x) = 11 - (5x/5x^2 + 7x - 12)

I think you meant

f(x) = 11 - 5x/(5x^2 + 7x - 12) which factors to
f(x) = 11 - 5x/((x-1)(5x+12))

V.A. when the denominator is zero
---> x = 1, -12/5

H.A. what happens when x becomes ± "large"
the algebraic term at the end --> 0
so y = 11

I don't "see" any oblique asymptotes.

Thank you very much, I have been trying to solve this the entire day... It's so simple... for some reason, I keep on pulling the 5 out of the equation.... This helps a lot.... Thanks...

To find the vertical, horizontal, and oblique asymptotes of a function without looking at a graph, you need to understand the behavior of the function as x approaches certain values.

1) Vertical Asymptote:
A vertical asymptote occurs when the value of x makes the denominator of the function equal to zero. In this case, the denominator is 5x^2 + 7x - 12. To find the vertical asymptotes, you need to solve the equation 5x^2 + 7x - 12 = 0 for x. Factor the quadratic equation or use the quadratic formula to find the values of x that make the denominator zero. These will be the x-values where the function has vertical asymptotes.

2) Horizontal Asymptote:
To find the horizontal asymptote, you need to consider the degree of the numerator and the denominator of the function. In this case, the numerator is 11 - (5x/5x^2 + 7x - 12). The highest power of x in the numerator is x^1, and the highest power of x in the denominator is x^2. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0 or the x-axis.

3) Oblique Asymptote:
An oblique asymptote occurs when the degree of the numerator is exactly one greater than the degree of the denominator. In this case, the degree of the numerator (1) is less than the degree of the denominator (2); therefore, there is no oblique asymptote.

By applying these principles to the given equation, you can find the vertical asymptotes (if any), horizontal asymptote, and determine whether or not there is an oblique asymptote.