Question

if an equation has x^2 or y^2 will it always be not a function?

Answer 1

is x^2+y^2=0 a function?

Answer 2

is that the question exactly as it is written?

Answer 3

in general

Answer 4

like x^2+1=y
or y^2+5=x

anything that's squared of x or y.

Answer 5

"will it always not be a function"?!

Answer 6

\[y=x^2+1\] is not a function, it is an equation
but the function
\[f(x)=x^2+1\] is a function

Answer 7

y=x^2+1 is a function
y^2+5=x isn't a function
x^2+y^2=0 is a function
x^2+y^2=1 isn't a function

Answer 8

i must disagree with my learned colleague @freckles

Answer 9

well a function of x that is

Answer 10

and also y is a function of x

Answer 11

disagree with me? on which one?

Answer 12

y=x^2+1 is a function

Answer 13

i mean is a function of x

Answer 14

i think that's a function

Answer 15

oh because i put y instead of f(x)

Answer 16

\[\{(x,y):y=x^2+1\}\] is a function

\[f(x)=x^2+1\] is a function
\[f:=x\to x^2+1\] is a function

Answer 17

because anything squared is positive?

Answer 18

\[y=x^2+1\] is an equation

Answer 19

no it has nothing to do with positive or negative

Answer 20

y can represent f(x)

Answer 21

a function is a rule that assigns to each element in one set (the domain) a unique element in another set (range, or codmain)

Answer 22

make that codomain
in any case the equation given by
\[x^2+y^2=1\] does not represent a function as @freckles said, because there can be two different y values for the same x value

Answer 23

http://www.mathsisfun.com/sets/function.html

Answer 24

wait so there can't be 2 or more x values that can give the same y?

Answer 25

http://tutorial.math.lamar.edu/Classes/Alg/FunctionDefn.aspx

Answer 26

both of these links say equations can be functions

Answer 27

and i like paul a lot

Answer 28

im confused with the definition of functions

Answer 29

the definition i got is that a relation for which every element in the domain has a unique corresponding element in the range? but a range can be the same?

Answer 30

if there are multiple ranges that are the same, wouldn't that be not unique?

Answer 31

Well this is the way Paul and I would define a function:
A function is an equation for which any x that can be plugged into the equation will yield exactly one y out of the equation.

Answer 32

In general, just remember that when looking at an equation in two variables x (independent variable) and y (dependent variable), the equation always represents a function as long as
i). the exponent of y is 1 and
ii). any term is either "+" ve or "-"ve but not both +/-

Answer 33

can you give an example of ii)? @calculusfunctions

Answer 34

@freckles when wouldn't a function yield one y?

Answer 35

Pretend we have x^2+y^2=1
This is not a function.
For example if x=0 then y^2=1 which means y=1 or y=-1
So we have (0,1) and (0,-1) are on the circle.
But look we have an x value yielding two different y-values
So this x^2+y^2=1 is definitely not a function.

Answer 36

ok, so whenever i see y^2, it will never be a function? if there is x

Answer 37

y^2=x-5
is not a function.
Example, if x=6, we have y^2=6-5=1 which means y=1 or y=-1
so we have (6,1) and (6,-1) on the parabola.
So we have an x yielding two different y-values.

Answer 38

Well x^2+y^2=0 is a function

Answer 39

And I say this because over the reals (0,0) is the only point on the graph of x^2+y^2=0

Answer 40

Some examples of functions:\[y =x ^{2}-3\]
\[y=\sqrt{x}\]
\[x ^{3}-2xy +3=0\]
\[y =\frac{ 1 }{ x }\]Examples of some equations that are not functions:\[4x ^{2}-y ^{2}=36\]
\[y =\pm \sqrt{x}\]
\[x ^{2}+y ^{2}\]

Answer 41

so can i check if an equation is a function by solving for x and see if it comes out to 2 or more y values?

Answer 42

Oops, I forgot to finish the last one\[x ^{2}+y ^{2}=25\]

Answer 43

You have to pick an x such that happens to show it is not a function
not just any x

Answer 44

@polarpenguin did you understand what I said?

Answer 45

so a function can't have +/- together?

Answer 46

Yes

Answer 47

That is correct

Answer 48

Do you think g(x) is a function?