Question

Pre-Calculus help??? Urgent

Answer 1

Write a rational function with a vertical asymptote of x=5 and a horizontal asymptote of y=1/2

Answer 2

vertical asymptotes occur when you divide by zero. to make an equation divide by zero when x = 5 you would need:
\[\huge\frac{1}{x-5}\]
now when x approaches 5, the denomenator approaches 0, and the function approaches infinity.

Answer 3

however, as the x value approaches infinity, the function will tend towards zero (dividing by infinity) so you would have to add 1/2 to every thing to ensure that it tends towards 1/2
\[\huge\frac{1}{x-5}+\frac{1}{2}\]
\[\huge\frac{2 + (x-5)}{2(x-5)}=\frac{x-3}{2x-10}\]

Answer 4

Thank you so much!