Function 2: Write a rational function that has at least two vertical asymptotes, no holes and no horizontal asymptote.

Question

Write the function in factored form and then write it in standard form. List the vertical asymptotes.  Describe the end behavior of the function.

Answer 1

x^4/((x-1)(x+1)) = x^4/((x^2-1) It has vertical asymptotes at x = ±1, no holes, and no horizontal asymptote.

Answer 2

I will not write this function for you, but I will tell you how to do it.

The exponent highest power of x in the numerator must be greater than the exponent of the highest power in the denominator so that the function "blows up" as |x| gets large.

The vertical asymptotes will occur at zeros of the denominator, i.e. factor of (x-a) in the denominator with no matching factor in the numerator.