Question

TuringTest, functions?

Answer 1

Right, so now that we've covered a lot of that let's look for something tricky:
starting simple:
y=x+7
is y a function of x?

Answer 2

Yes

Answer 3

good
now, is x a function of y ?

Answer 4

No

Answer 5

Cause x is the dependent variable

Answer 6

x is the independent variable, but the independent variable can be a function of the dependent variable sometimes. It can work both ways. Not always, though. You must check.

to find out try solving for x above

Answer 7

y=x+7
y-7=x?

Answer 8

so is x a function of y?

Answer 9

can we switch their places?

Answer 10

They should work both ways.

Answer 11

right, so in
y=x+7
we can write one variable as a function of the other at will
x=y-7
so we can change the way we look at this and call it
f(x)=x+7=y
or
g(y)=y-7=x
they are both functions and both equivalent.

now trickier:
what about

y=x^2
is y a function of x ?

Answer 12

Yes?

Answer 13

yes, each x gives exactly one y
now the hard part :P
is x a function of y?

Answer 14

No, cause each y gives us 2 x

Answer 15

It could be a function of yx

Answer 16

how so? elaborate ;)

Answer 17

every element of a is maped to an element of b