What is the range and inverse of the function y = 1/x?

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Discussion Overview

The discussion centers on determining the range and inverse of the function y = 1/x. Participants explore algebraic methods, graphical interpretations, and the implications for novice learners, focusing on both theoretical and conceptual aspects.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant attempts to find the range algebraically and concludes that the range is all real numbers except y = 0, seeking confirmation of this result.
  • Another participant suggests sketching the graph of y = 1/x to answer the question, implying that visual representation may aid understanding.
  • A different participant expresses concern about the meaning of the graph for novice learners, noting the behavior of the function in quadrants 1 and 3 and referencing a textbook answer for the range.
  • One participant points out that a similar question was asked in another forum post, indicating a potential overlap in discussions.

Areas of Agreement / Disagreement

There is no clear consensus on the range and inverse of the function, as participants present differing approaches and interpretations without resolving the discussion.

Contextual Notes

Participants express varying levels of understanding regarding the implications of the graph and the algebraic findings, with some assumptions about the audience's familiarity with the concepts remaining unaddressed.

Who May Find This Useful

This discussion may be useful for students learning about functions, particularly those interested in understanding the range and inverse of rational functions, as well as educators seeking to clarify these concepts for novice learners.

mathdad
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Find the range algebraically.

y = 1/x

Find inverse of y.

x = 1/y

Solve for y.

yx = (1/y)(y)

yx = 1

y = 1/x

f^(-1) x = 1/x

The domain of f^(-1) x is ALL REAL NUMBERS except that x cannot be 0.

So, the range of y = 1/x is ALL REAL NUMBERS except that y cannot be 0.

Correct?
 
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$y = \dfrac{1}{x}$ is a basic parent function whose graph is easily sketched ... so, sketch it and answer your own question.
 
I know what this graph looks like. I've seen it hundreds of times but what does it mean to a novice math learner? There is a curve in quadrants 1 and 3 that does not cross the lines x = 0 and y = 0. The textbook answer is (-infinity, 0) U (0, infinity). What on the graph tells me that this is the correct range?
 
you asked the same question in your other post ...

http://mathhelpboards.com/pre-calculus-21/range-functions-4-a-21775.html#post98495
 

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