# Homework Help: Which of the following represent a function

1. Jun 4, 2015

### Jaco Viljoen

1. The problem statement, all variables and given/known data
Which of the following represent a function:
a)$$y=-1/2x+3$$

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

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

2. Relevant equations

3. 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

Last edited: Jun 4, 2015
2. Jun 4, 2015

### 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.

3. Jun 4, 2015

### Jaco Viljoen

Hi Thermo,
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...

4. Jun 4, 2015

### Thermo

Yes I realised it later sorry for that. So the answer must be only c is a function. However domains and codomains matter in this case.

5. Jun 4, 2015

### Jaco Viljoen

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

6. Jun 4, 2015

### SammyS

Staff Emeritus
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.

7. Jun 4, 2015

### 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.

8. Jun 4, 2015

### SammyS

Staff Emeritus
That U shape is called a parabola.

What is the graph of equation (a) called ?

9. Jun 4, 2015

### Thermo

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

10. Jun 4, 2015

### Jaco Viljoen

a Hyperbola

11. Jun 4, 2015

### Jaco Viljoen

no problem, Luckily there are many smart guys and gals to double check one another.

12. Jun 4, 2015

### 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.

13. Jun 4, 2015

### cnh1995

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..

Last edited: Jun 4, 2015
14. Jun 4, 2015

### Jaco Viljoen

From my text book:
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.

15. Jun 4, 2015

### 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

16. Jun 4, 2015

### Jaco Viljoen

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

Last edited: Jun 4, 2015
17. Jun 4, 2015

### cnh1995

Well is it due this "precalculus" concept? Because as per my knowledge, these are all treated as functions in calculus.

18. Jun 4, 2015

### SammyS

Staff Emeritus
These three equations might be treated in Calculus, but equation (b) better not be referred to as a function.

19. Jun 4, 2015

### Staff: Mentor

The first one, which I am assuming is y = -(1/2)x + 3, is a function, and is one-to-one.

20. Jun 4, 2015

### Staff: Mentor

That is just function notation, but isn't any sort of basic equation.
No, not all of them are functions.
The equation in a) is a continuous function. In clearer form, the equation is y = -(1/2)x + 3.

21. Jun 4, 2015

### Staff: Mentor

Sammy is correct.

22. Jun 4, 2015

### Thermo

I suppose it is 1/(2x)

23. Jun 4, 2015

### Staff: Mentor

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.

24. Jun 5, 2015

### Jaco Viljoen

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

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

25. Jun 5, 2015

### SammyS

Staff Emeritus
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 ?