The domain and range of the function are x < 5 U x > 5 and y < 4 U y > 4, respectively
How to determine the domain and range of the function
From the question, we have the following parameters that can be used in our computation:
f(x) = 2/(x - 5) + 4
For the domain, we set the denominator of the fuction not equal to 0
So, we have
x - 5 ≠ 0
Evaluate
x ≠ 5
This can be represented as
x < 5 U x > 5
For the range, we have to to be all real values except at the asymptote
This means that we set the fractional term to 0
So, the range is
y ≠ 0 + 4
y ≠ 4
This can be represented as
y
The graph of the function is attached