Write the equation of a function with the following requirements: A domain of all real numbers over 3, a range of all real numbers, an x-intercept of (5,0), and a vertical asymptote at x = 3.

Answer 1

(x-5) will cross x axis at 5

1/(x-3) goes nuts at 3

so try

f(x) = (x-5)/(x-3)
check domain and range
any x except x = 3 so domain ok
now sketch a graph to see range
if x is big + or -, f(x) = 1
if x is little less than 3, f(x)--> -oo
if x is a little more than 3, f(x)->+oo
and is 0 at x = 5
so range is all real numbers, ok
if x is a little less than

Answer 2

How about

vertical asymptote at x=3, domain is x>3, x-intercept of (4,0)
y = log(x-3)

to move the intercept to (5,0), we need to double the distance from the asymptote to the intercept.
y = log((x-3)/2)

see

http://www.wolframalpha.com/input/?i=log(1%2F2+(x-3))+for+x%3E3