Question

If the function y=1/x is translated to the left 2 units and up 6 units, what is the new horizontal asymptote

Answer 1

y=6

Explanation:

The horizontal asymptote for y = 1/x is the x-axis, y = 0.

Shifting the graph up 6 makes the asymptote move up, too, to y = 6.

See the attached image:

y = 1/x is purple

y = 1/(x + 2) + 6 is black