Function Algebra

[babadoctor]

I am confused

 

is this picture about a function correct?

not a function when there is multiple domains to one range?

[skyress3000]

It's not a 1 to 1 function, but it is a function

[Admiral Naismith]

Yes. One to one means that every value in the range has only one corresponding value in the domain, and vice versa.

[79wjd]

Function 1 is an onto function, but not one to one while function two is onto and one to one. 

 

y=x² has two x values for the each y and is a function. A function can't have multiple y values for the same x (x=y² is not a function).

[Speedyv]

In a function, each domain only has one range.

 

So, for each x-value, there is only one y-value. 

 

[Speedyv]

It's not a 1 to 1 function, but it is a function

 

It can't be expressed as a function at all if there is more than one range for an input. 

[skyress3000]

It can't be expressed as a function at all if there is more than one range for an input. 

Yes - I know. This function has more than one domain for a range, meaning it's not one to one even though it is a function.

[babadoctor]

Thanks guys!

[Speedyv]

Yes - I know. This function has more than one domain for a range, meaning it's not one to one even though it is a function.

 

But you can't call it a function in the first place....

[skyress3000]

But you can't call it a function in the first place....

Yeah... you can. There is no instance where any domain maps to multiple inputs. Therefore I can define it as a piecewise function like so:

if x = 2 f(x) = 9

if x = 4 f(x) = 5

if x = 11 f(x) = 5

I think you'll find the function I just gave satisfies the example in the original image, so the example must be a function.

[Speedyv]

Yeah... you can. There is no instance where any domain maps to multiple inputs. Therefore I can define it as a piecewise function like so:

if x = 2 f(x) = 9

if x = 4 f(x) = 5

if x = 11 f(x) = 5

I think you'll find the function I just gave satisfies the example in the original image, so the example must be a function.

 

Yeah I realized I didn't read the first post thoroughly enough haha

 

It's sort of irrelevant to say it's not a one to one function if there are more than one y-values for different domains. It's usually backwards  :wacko: