Which of the following represent a function

  • Thread starter Jaco Viljoen
  • Start date
  • Tags
    Function
In summary: These three equations might be treated in Calculus, but equation (b) better not be referred to as a function because it does not meet the vertical line test.
  • #1
Jaco Viljoen
160
9

Homework Statement


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

b)[tex]x^2+y^2=25[/tex]

c)[tex]y=2x^2+7x+3[/tex]

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
 
Last edited:
Physics news on Phys.org
  • #2
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
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...
 
  • #4
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.
 
  • Like
Likes Jaco Viljoen
  • #5
Would I be able to solve the equation to prove this?
 
  • #6
Jaco Viljoen said:

Homework Statement


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

b) [itex]\ \ x^2+y^2=25[/itex]

c) [itex]\ \ y=2x^2+7x+3[/itex]

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.
 
  • Like
Likes Jaco Viljoen
  • #7
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
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 ?
 
  • Like
Likes Jaco Viljoen
  • #9
Sorry for the wrong info I wasn't so sure I think I am mistaken for continuity or differentiability.
 
  • Like
Likes Jaco Viljoen
  • #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.
 
  • Like
Likes Thermo
  • #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..
 
Last edited:
  • #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.
 
  • Like
Likes cnh1995
  • #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
 
  • Like
Likes cnh1995
  • #16
A and C because B is not a function.
I am not sure anymore.
 
Last edited:
  • #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.
 
  • Like
Likes cnh1995 and Jaco Viljoen
  • #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..
 
  • Like
Likes Jaco Viljoen
  • #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.
 
  • Like
Likes Jaco Viljoen
  • #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.
 
  • Like
Likes Jaco Viljoen
  • #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 ?
 
  • Like
Likes Jaco Viljoen
  • #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.
 
  • Like
Likes SammyS

FAQ: Which of the following represent a function

1. What is a function?

A function is a mathematical relationship between two sets of numbers, where each input (or independent variable) maps to exactly one output (or dependent variable).

2. How can I tell if a given set of points represents a function?

To determine if a set of points represents a function, you can use the vertical line test. If a vertical line can be drawn through the graph and only intersects the graph at one point, then the set of points represents a function. If the vertical line intersects the graph at more than one point, then the set of points does not represent a function.

3. Can a function have more than one output for a given input?

No, by definition, a function can only have one output for each input. If there are multiple outputs for a given input, then the relationship between the two sets of numbers is not a function.

4. What is the difference between a linear and non-linear function?

A linear function is a function where the output varies in direct proportion to the input. This means that the graph of a linear function is a straight line. On the other hand, a non-linear function is a function where the output does not vary in direct proportion to the input. The graph of a non-linear function is not a straight line.

5. How are functions used in real life?

Functions are used in various fields, such as engineering, physics, economics, and statistics, to model and analyze relationships between different variables. For example, in economics, functions are used to represent the relationship between supply and demand. In physics, functions are used to describe the motion of objects. In everyday life, functions can also be used to calculate things like interest rates, distances, and probabilities.

Back
Top