please help
what is the equation for the horizontal asymptote

d) (5,1)
e) y=2
f) x-5
d, f) The "hole" is the little circle on the graph at (5, 1) indicating the function is not defined there. It means there is a factor of (x-5) in the denominator that makes the denominator zero at that point.
The vertical asymptote this would normally create is canceled by a zero at x=5, that is, the numerator also has a factor of (x-5).
e) The equation of the horizontal dashed line with a y-intercept of 2 (the horizontal asymptote) is y=2.