Question 466391
 Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph. 
f(x)=1/(x-5)³+1
...
Horizontal Asymptote:
When the degree of the numerator is less than the degree of the denominator, as in this case, the horizontal asymptote is the x-axis or y=0.
..
To find the vertical asymptote set the denominator=0, then solve for x.
(x-5)^3+1=0
(x-5)^3=-1
Take cube root of both sides
x-5=-1
x=5-1=4
Vertical asymptote: x=4
..
Domain: (-∞, 4) U (4, ∞)
Range: (-∞, 0) U (0, ∞)
See the graph below as a visual check on the answer.

..
y=1/((x-5)^3+1)
{{{ graph( 300, 300, -10, 10, -4, 4,1/1/((x-5)^3+1)) }}}