# Thread: how to graph this function

1. ## how to graph this function

https://imgur.com/lK1xqqU

so (i) is just a parabola. (iv) is a parabola, but only on the right hand side, so where x is a non-negative real number.

How would I graph (ii) and (iii)

For instance, for (ii) the function has a domain of non-negative real numbers, but has a co-domain of all real numbers.

Or (iii) function has a domain of real numbers but codomain of non-negative real numbers.

2. ## Re: how to graph this function

Originally Posted by math951
https://imgur.com/lK1xqqU
so (i) is just a parabola. (iv) is a parabola, but only on the right hand side, so where x is a non-negative real number.
How would I graph (ii) and (iii)
For instance, for (ii) the function has a domain of non-negative real numbers, but has a co-domain of all real numbers.
Or (iii) function has a domain of real numbers but codomain of non-negative real numbers.
Note that the graphs of (II), & (IV) are identical, but the functions are different.

3. ## Re: how to graph this function

For two functions to be equal, they must have the same domain, codomain, and image. Clearly, these four are not the same functions, but you are telling me that these four are all the same graph?

4. ## Re: how to graph this function

So domain is all values of x essentially (the input). And Codomain is all possible output values of y. Range is different from codomain, because codomain is all possible output values, whereas, range is just the actual output values. So our function is f(x)=x^2

we know that x^2=0. So, y has to be greater than or equal to 0!

So with this in mind, if we have the function from the set of non-negative real numbers to the set of real numbers defined by f(x)= x^2...this means that, our x input has to be x greater than or equal to 0. And our codomain is all real numbers.... but we know y has to be greater than or equal to 0...