Which Relation Fails the Function Test?

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Discussion Overview

The discussion revolves around identifying which of several mathematical relations does not qualify as a function. Participants explore the definitions and characteristics of functions, particularly focusing on the conditions under which a relation can be expressed as a function of x.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • Some participants emphasize that a function must have only one output value for each input value of x.
  • One participant mentions the 'vertical line test' as a method to determine if a relation is a function.
  • Another participant suggests that if a relation can be expressed in the form y = f(x), it qualifies as a function, implying that one of the given relations does not meet this criterion.
  • A participant questions whether substituting values for x can help determine if a relation is a function.
  • There is a suggestion to solve the relations for y to identify which one may yield multiple outputs for a single input.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, with no consensus on which specific relation fails the function test. The discussion remains unresolved regarding the identification of the non-function.

Contextual Notes

Some participants reference the vertical line test and the need to express relations in the form y = f(x), but the application of these concepts is not fully explored or agreed upon.

melissax
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Hi, I have a question and couldn't solve.
Can you help me?
Which one isn't function how i can show?

(a) y = |x^3 + 5|
(b) y = x2 + sqrt(x) -sin(x)
(c) y2 = (x-5)^2 + 10
(d) y3 = x + 4

Thank you?
 
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Re: Which one isn't function?

melissax said:
Hi, I have a question and couldn't solve.
Can you help me?
Which one isn't function how i can show?

(a) $y = |x^3 + 5|$
(b) $y = x^2 + \sqrt(x) -\sin(x)$
(c) $y^2 = (x-5)^2 + 10$
(d) $y^3 = x + 4$

Thank you?
The essential thing about a function is that there should be only one value of $y$ for each value of $x$. Can you see one of those formulas where there might be more than one value of $y$ for a given value of $x$?
 
Re: Which one isn't function?

melissax said:
Hi, I have a question and couldn't solve.
Can you help me?
Which one isn't function how i can show?

(a) y = |x^3 + 5|
(b) y = x2 + sqrt(x) -sin(x)
(c) y2 = (x-5)^2 + 10
(d) y3 = x + 4

Thank you?
You should have been taught the 'vertical line test' ...
 
Re: Which one isn't function?

should i give value to the x?

If i give can i understan is function or not?
 
Re: Which one isn't function?

If the given relation can be expressed as $\displaystyle y=f(x)$, then it is a function. Only one of the given relations cannot be written this way.

Try solving them for y, and which one gives you more than one possible function?
 

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