The transformed function can be written as g(x) = -1/(x - 4) + 2
How to find the function:
We want to find the equation for:
y = 1/x = f(x)
When:
(1) Reflect about the x-axis (2) Shift up 2 units (3) Shift right 4 units
First, a reflect about the x-axis just means that we need to multiply by -1, then:
g(x) = -f(x)
A shift up of 2 units means that we need to add 2.
g(x) = -f(x) + 2
A shift right of 4 units means that we need to subtract 4 i the argument:
g(x) = -f(x - 4) + 2
Then we can write:
g(x) = -1/(x - 4) + 2