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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

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

How we find the range of this rational function without a calculator?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,610

It's got a vertical asymptote at x=3. And a horizontal one at y=1.

If you attempt to solve for y=1 you get no x value.

So that's a clue. Try to construct the graph

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

Bob wrote:

It's got a vertical asymptote at x=3. And a horizontal one at y=1.

If you attempt to solve for y=1 you get no x value.

So that's a clue. Try to construct the graph

Bob

The whole idea here is to find the range algebraically not using a graph. I don't recall much about asymptotes. Asymptotes is still a few sections away in my self-study of precalculus. Simply looking for an algebraic solution. Someone hinted that the domain of the inverse function is the range of the given function. Is that true?

1. Find the inverse of the given function.

2. Find the domain of the inverse function found.

You say?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,610

That should work but I still think the graph is the key. Once you have that the algebra is easy.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**sologuitar****Member**- Registered: 2022-09-19
- Posts: 467

Bob wrote:

That should work but I still think the graph is the key. Once you have that the algebra is easy.

Bob

Graphing is ok but I am more interested in algebra manipulation.

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