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do u remember the definition of function?

A function is a rule that assigns a unique element in Rn to Rm. It is one to one.

the last part is something else.

a function assigns a UNIQUE element to EVERY element of its domain.

Ok I understand that.

So a certain w and x cannot have two outputs.

what does (w,x)=(1,-1) get assigned to?

yes. precisely.

(1,-1) is assigned to (1,1)?

just that?

let's see:
\[ \large y=w=1 \]
right?

right

BUT
\[ \large z^4=x^2=(-1)^2=1\Rightarrow z=\pm\sqrt[4]{1}=\pm1 \]

so
\[ \large (1,-1)\mapsto(1,1) \]
and
\[ \large (1,-1)\mapsto(1,-1) \]

So does that mean T is not a function?

yes. that's what u were asked to prove.

T is graph of something, but that something is not a function. right?

yes.

Thank you SO much!

u r welcome.