What Determines the Range of a Rational Function Like f(x) = 2/(x - 3)?

[mathdad]

Find the range of
f(x) = 2/(x - 3).

1. What exactly are we looking for when we say RANGE of a rational function?

2. Is the domain of the inverse the range of the given function?

3. What is the easiest way to find the range? Graphing?

 

[Greg]

1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).

 

[mathdad]

1. All the values a function assumes over its domain.

2. Let's see:

y = 2/(x - 3)

x - 3 = 2/y

x = 2/y + 3

y^(-1) = 2/x + 3

What conclusions may we draw? (look at the values 3 and 0 in both functions).

3. Depends on the function (in my opinion).

I do not understand your answer to question 1.
I also do know what conclusions we can draw based on the values of 3 and 0 in both functions.