Subject: Range of a function

Hello. My name is David Bell, and I am a high school math teacher in New Delhi, India. As part of a technology class, I am learning how to "Ask the online experts." My question is: Given a rational function such as f(x) = (8x-3)/(4x-1). How can the range be found. We know that the Domain is that x can't be 1/4, but short of looking at limits as x approaches infinity, how can the range be determined. Thanks for your help

David Bell

Hi David,

I find it interesting that this question comes from a technology class, as this is a problem where technology can help. Using a graphing calculator or a graphing program on a computer can be a big help in finding, or at least estimating, the domain and range of a function.

For your particular problem you can find the inverse of the function, and then the domain of the inverse is the range of the original function. The function you have is:

y = f(x) = (8x-3)/(4x-1)

To find the inverse, interchange the role of x and y and then solve for y.

x = (8y-3)/(4y-1)
4xy - x = 8y - 3
y = (x - 3)/(4x - 8)

The domain of this function is all x except x = 2 and hence the range of f(x) = (8x-3)/(4x-1) is all x except x = 2.

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