Which of the following represent a function

[Jaco Viljoen]

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

 

[Thermo]

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.

 

[Jaco Viljoen]

Hi Thermo,
Thank you for your reply,

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...

 

[Thermo]

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.

 

[Jaco Viljoen]

Would I be able to solve the equation to prove this?

 

[SammyS]

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.

 

[Jaco Viljoen]

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.

 

[SammyS]

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 ?

 

[Thermo]

Sorry for the wrong info I wasn't so sure I think I am mistaken for continuity or differentiability.

 

[Jaco Viljoen]

That U shape is called a parabola.

What is the graph of equation (a) called ?

a Hyperbola

 

[Jaco Viljoen]

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.

 

[Jaco Viljoen]

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.

 

[cnh1995]

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..

 

[Jaco Viljoen]

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.

 

[Jaco Viljoen]

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

 

[Jaco Viljoen]

A and C because B is not a function.
I am not sure anymore.

 

[cnh1995]

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.

 

[SammyS]

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.

 

[Mark44]

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.

 

[Mark44]

Basic equation of a function is y=f(x)..

That is just function notation, but isn't any sort of basic equation.

Aren't all of them functions??

No, not all of them are functions.

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.

They are just the types of function..

 

[Mark44]

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.

Sammy is correct.

 

[Thermo]

I suppose it is 1/(2x)

 

[Mark44]

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.

 

[Jaco Viljoen]

(-1/2)x + 3, not -1/(2x) + 3
as mark says,

Sorry for the typo, still getting used to typing like this.

 

[SammyS]

(-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.

a Hyperbola

which was in response to

...

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 ?

 

[Jaco Viljoen]

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.