I'm getting confused on how to answer these questions and need help to see if I'm doing it right

Question

Find the specified asymptotes of the following functions. Recall that asymptotes are lines therefore the answer must be given as an equation of a line. All should be done with answers, show work, explain in words.

a) Find the vertical asymptote of the function f(x) = 4 over x + 5

b) Find the horizontal asymptote of the function g(x) = 5x^2 -4  over x + 1

c) Find the vertical and horizontal asymptote of the function f(x) = 3x – 1 over x +4

#c needs both answers and show work and explain in words.

d) Find the vertical and horizontal asymptote of the function g(x) = _x + 7_ over x² - 4

#d needs both answers and show work and explain in words.

Answer 1

Hi Char, 

       I can't add anything more to the above answers....they make sense to me. What might help you though, if you want to spend the time, is to make a graph of each of the functions for a number of x values. This is easy to do in Excel. The first function f(x)=4/(x+5) when you graph it you will notice that when you choose x=2 you get f(2)=4/7 at x=0 f(0)=4/5 and at x=-2 f(-2)=4/3 and x=-4 f(-4)= 4 x=-4.9 f(-4.9)=40 WOW f(x) really get big fast as x get near 5 so x=5 is a vertical line which is called the asymptote. 

Hope this helps

Jim

Answer 2

To find the vertical asymptotes, set the denominator equal to 0 and solve for x (ex. x+5=0). To find the horizontal asymptotes, look at the exponents in both the numerator and the denominator. If the exponent is bigger on bottom, (ex. 3x+4 over x^2+7) then the horizontal asymptote is 0. If the exponent is bigger on top, (ex. x^2-1 over x+3) then there are no horizontal asymptotes. However, if the exponents are the same for both the numerator and the denominator, (ex. 2x^2+x+5 over x^2+2) then you divide the coefficients--in this case, 2 divided by 1--which will equal 2, giving you your horizontal asymptote: y=2.