Which of the following represent a function

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Homework Help Overview

The discussion revolves around determining which of the provided equations represent functions. The equations in question include linear and quadratic forms, as well as a circle equation, prompting participants to analyze their characteristics in relation to function definitions.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the definitions of functions, particularly focusing on the vertical line test and the uniqueness of y-values for given x-values. There are attempts to clarify the nature of the equations and their graphical representations, with some questioning the interpretations of the equations.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have offered insights into the nature of the equations, while others express confusion about the definitions and characteristics of functions. There is no explicit consensus on the classification of all equations as functions.

Contextual Notes

Participants mention the importance of domain and codomain in determining whether the equations qualify as functions. The discussion also touches on the distinction between functions and one-to-one functions, with references to calculus and precalculus concepts.

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Homework Statement


Which of the following represent a function:
a)y=-1/2x+3

b)x^2+y^2=25

c)y=2x^2+7x+3

Homework Equations

The Attempt at a Solution


a)
b) is a circle so has 2 values for y and is not a function.
c)
I know that functions only have 1 y relation to x but don't know how to prove whether a and c are functions or not.
Thank you
 
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If domain and codomain of the functions are f: R-->R . Then "a" can't be function because there is no answer for x=0. And also like you said b can't be a function because there are two reflections of x=a.
 
Hi Thermo,
Thank you for your reply,
Thermo said:
If domain and codomain of the functions are f: R-->R . Then "a" can't be function because there is no answer for x=0. The others can be a function.
Others? meaning b and c?
I don't agree or I am missing the plot.
B cannot be a function because it is a circle...
 
Yes I realized it later sorry for that. So the answer must be only c is a function. However domains and codomains matter in this case.
 
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Would I be able to solve the equation to prove this?
 
Jaco Viljoen said:

Homework Statement


Which of the following represent a function:
a) \ \ y=-1/2x+3

b) \ \ x^2+y^2=25

c) \ \ y=2x^2+7x+3

Homework Equations



The Attempt at a Solution


a)
b) is a circle so has 2 values for y and is not a function.
c)
I know that functions only have 1 y relation to x but don't know how to prove whether a and c are functions or not.
Thank you
By the way: Thermo is incorrect.

What you have for (a) literally means ##\displaystyle\ y=-\frac{1}{2}x+3\ .\ ## Is that what you mean?

Or do you mean ##\displaystyle\ y=-\frac{1}{2x}+3\ ?\ ##

You can graph the equations , (a) and (c) .

You should be able to identify what figures the graphs produce.
 
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Hi Sammy,
you are correct,
I get a u shape for c
and upside down u shape for a.

So a and c are functions.
Thank you so much for your input.
 
Jaco Viljoen said:
Hi Sammy,
you are correct,
I get a u shape for c
and upside down u shape for a.

So a and c are functions.
Thank you so much for your input.
That U shape is called a parabola.

What is the graph of equation (a) called ?
 
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Sorry for the wrong info I wasn't so sure I think I am mistaken for continuity or differentiability.
 
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  • #10
SammyS said:
That U shape is called a parabola.

What is the graph of equation (a) called ?
a Hyperbola
 
  • #11
Thermo said:
Sorry for the wrong info I wasn't so sure I think I am mistaken for continuity or differentiability.
no problem, Luckily there are many smart guys and gals to double check one another.
 
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  • #12
there is a second part to the question:
which statements do not define a one-to-one function?

My answer is B because it is a circle and not a function.
 
  • #13
Jaco Viljoen said:
there is a second part to the question:
which statements do not define a one-to-one function?

My answer is B because it is a circle and not a function.
Basic equation of a function is y=f(x).. Aren't all of them functions?? B isn't a one to one function and A isn't a continuous function.. They are just the types of function..
 
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  • #14
From my textbook:
A function f between two sets of real numbers A and B is a relation in which each element of A is paired with a unique element of B.

If you draw a vertical line on the graph, is it possible that the line can intersect the graph at 2 places? If it does the equation is not a function.
 
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  • #15
Although,
The function y = f(x) is a function if it passes the vertical line test. It is a one-to-one function if it passes both the vertical line test and the horizontal line test.

Then none of these are a 1-1 function.

Could someone agree/disagree with this?
Thank you,

Jaco
 
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  • #16
A and C because B is not a function.
I am not sure anymore.
 
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  • #17
Jaco Viljoen said:
From my textbook:
A function f between two sets of real numbers A and B is a relation in which each element of A is paired with a unique element of B.

If you draw a vertical line on the graph, is it possible that the line can intersect the graph at 2 places? If it does the equation is not a function.
Well is it due this "precalculus" concept? Because as per my knowledge, these are all treated as functions in calculus.
 
  • #18
cnh1995 said:
Well is it due this "precalculus" concept? Because as per my knowledge, these are all treated as functions in calculus.
These three equations might be treated in Calculus, but equation (b) better not be referred to as a function.
 
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  • #19
Jaco Viljoen said:
Although,
The function y = f(x) is a function if it passes the vertical line test. It is a one-to-one function if it passes both the vertical line test and the horizontal line test.

Then none of these are a 1-1 function.

Could someone agree/disagree with this?
The first one, which I am assuming is y = -(1/2)x + 3, is a function, and is one-to-one.
 
  • #20
cnh1995 said:
Basic equation of a function is y=f(x)..
That is just function notation, but isn't any sort of basic equation.
cnh1995 said:
Aren't all of them functions??
No, not all of them are functions.
cnh1995 said:
B isn't a one to one function and A isn't a continuous function..
The equation in a) is a continuous function. In clearer form, the equation is y = -(1/2)x + 3.
cnh1995 said:
They are just the types of function..
 
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  • #21
cnh1995 said:
Well is it due this "precalculus" concept? Because as per my knowledge, these are all treated as functions in calculus.
SammyS said:
These three equations might be treated in Calculus, but equation (b) better not be referred to as a function.
Sammy is correct.
 
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  • #22
I suppose it is 1/(2x)
 
  • #23
Thermo said:
I suppose it is 1/(2x)
I believe it was meant as (-1/2)x, not (-1)/(2x). @Jaco hinted that my thought is correct, but he didn't explicitly say that.

In any case, what he wrote was this: y=−1/2x+3. The correct interpretation of this is (-1/2)x + 3, not -1/(2x) + 3.
 
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  • #24
(-1/2)x + 3, not -1/(2x) + 3
as mark says,

Sorry for the typo, still getting used to typing like this.
 
  • #25
Jaco Viljoen said:
(-1/2)x + 3, not -1/(2x) + 3
as mark says,

Sorry for the typo, still getting used to typing like this.
In that case, when you said the graph for equation (a) was a hyperbola, you were incorrect.
Jaco Viljoen said:
a Hyperbola
which was in response to
SammyS said:
...

What is the graph of equation (a) called ?
Equation (a) : ##\ y=(-1/2)x + 3\ ## gives the graph of a line with slope of ##\ -1/2\ ## .

By the way: Did you say that none of the equations gave a 1 to 1 function ?
 
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  • #26
SammyS said:
In that case, when you said the graph for equation (a) was a hyperbola, you were incorrect.

which was in response to

Equation (a) : ##\ y=(-1/2)x + 3\ ## gives the graph of a line with slope of ##\ -1/2\ ## .

By the way: Did you say that none of the equations gave a 1 to 1 function ?

Hi Sammy,
I realized It is not a hyperbola, was thinking of something I was watching.
It is a line it is a 1-1 function.
 
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