RANGE: Find the range of the function. In the space provided, type the answer without any spaces between the letters, numbers, or symbols.

Question

Answer 1

another solution is to find the inverse of the function and the domain of the inverse function is the range of the original function

y=2x/(x-11)

x=2y/(y-11)

x(y-11)=2y

xy-11x=2y

-11x=2y-xy

11x=-2y+xy

11x=y(x-2)

11x/(x-2)=y

y=11x/(x-2)

the domain is all real numbers except 2 so this is the range of the original function

Answer 2

"range" is defined as the possible values of the dependent variable. To find this, look at "end behavior"--AKA limits.

for this problem, h(x) becomes undefined at x = 11. Otherwise, look at what happens for large positive x. On the bottom, the -11 becomes insignificant, leaving just 2x/x = 2

For large negative x, the limit is also 2

Note that these are asymptotes, meaning that the function never actually gets there.

So, the range is simply h(x) ≠ 2

CHECK by graphing