University Algebra help

Question

Consider the function f(x) = ax2 + k/bx2 + h , where a, b, k, and h are all constants with a, b > 0.

a) What can you say about asymptotes and intercepts of the function if h, k > 0?

b) Now assume that k < 0 and h > 0. How does this affect the asymptotes? The intercepts?

c) If b = 1 and a > 1, how does this affect the results from part b?

d) How is the graph affected if k > 0 and h < 0?

e) Find values of a, b, k, and h that create a function with a horizontal asymptote at y = 3/2 , x-intercepts at (−5, 0) and (5, 0), a y-intercept of (0, −2) and no vertical asymptotes.

Answer 1

Jon, this might be fun to figure out, but we need a clarification from you first.

Is the function...

f(x) = ax^2 + (k/b)x^2 + h

or

f(x) = ax^2 + k/(bx^2) + h

or

f(x) = ax^2 + k/(2bx) + h

or something else.

I am asking, are the 2's exponents in both cases?

And what is the denominator of the second term? Just b... or bx^2.... or bx times 2 ?