_

Question

_

snowfire · Answer

What is a special feature of a function? (And by feature, I mean what is one attribute of a function, specifically the one that is relevant here?)

snowfire · Answer

I'll give you a hint, it has something to do with the input and output values.

pixiedust1 · Answer

The 5=5 and 1=1. 1 cannot equal 2?

snowfire · Answer

No, a function takes an input value (the value that is in the parentheses in front of the "f") and spits out a number. Since this is a function, what can be said about those inputs and outputs?

pixiedust1 · Answer

I have no idea

snowfire · Answer

Remember that pencil rule you used on graphs to figure out if it was a function or not?

pixiedust1 · Answer

Yeah

snowfire · Answer

Do you understand why that worked to find out if it was a function or not?

pixiedust1 · Answer

Yup

snowfire · Answer

So now apply that here. The pencil rule said that if the pencil, when held up vertically, does not collide with the line more than once, it is a function. That means that for every x, there is only one possible output (or y), right? Now do you know what the answer is?

pixiedust1 · Answer

Yes!!!!! f(2)=1, right?

snowfire · Answer

We are finding which answer cannot be true. If f(1)=5, what do we know will happen if we find f(1) again?

pixiedust1 · Answer

It will collide?

snowfire · Answer

It's a function, that means each and every x only has one y. x is 1 here, and the y is 5 for that x. So how can y be anything but 5?

pixiedust1 · Answer

True

snowfire · Answer

So which answer clearly breaks that rule?

pixiedust1 · Answer

f(5)=5?

snowfire · Answer

Imagine that on a graph. At x=1, y is 5. At x=5, y is 5. If you were to hold the pencil vertically, it wouldn't actually collide twice. If you held it horizontally, it would though. But that doesn't break the rule so it's fine.

pixiedust1 · Answer

f(1)=1 then?

pixiedust1 · Answer

Or no, because that would work too

snowfire · Answer

|dw:1384722117340:dw|

snowfire · Answer

That's what you would see if f(5)=5, just assuming anything in between is unnecessary

snowfire · Answer

Draw me a picture for each of the answers, to convince me you understand.

snowfire · Answer

But we are not done yet! T_T I drew the picture for f(5)=5, now draw me the other two graphs, and just put anything random at the places other than the points.

adilalvi · Answer

good job @Snowfire

snowfire · Answer

It might be helpful to use the "draw" option under where you are typing.

snowfire · Answer

No problem, and the answer is A since we ran out of time. That's because A is telling us that when x=1, y can be either 1 or 5. That is not a function.