Which function is not one-to-one?

[UrbanXrisis]

There is a Math problem that I got wrong and I want to know why it’s wrong:

X...(–2)..(–1)..0...1...2
F(X) 1...(–2)..0.(–1)..2
G(X) 3...(–2)..0.(–2)..3
H(X) 1...(–3)..0...3.(–1)

Which function is not one-to-one? I put all of them but got it wrong
Which function is symmetrical about the origin? is it H(X)?

how would I know if something is one-to-one without graphing it?
What about if a function is symmetrical about the origin?

 

[JasonRox]

You know if it is one-to-one if there is no duplicate value of "y".

Remember, the horizontal test? If it hits the graph twice when you test it as y=3, than there will be two solutions for x, when y=3. You do not want this.

Also, a function that is symmetrical about the origin is an odd function. An odd function is when f(-x)=-f(x).

I can barely tell what you wrote down. I don't see the significance of all the dots.

I am assuming that the top row is the values of x (domain), and the next three rows below are the range of the various functions.

By looking at F(x), we see that we none of the F(x) values are equal. Assuming that the function is just dots, than this function is one-to-one. If we must imagine a line being drawn from dot to dot, than it is NOT one-to-one.

EXPLAINED: We start at point (-2,1), then we go down to point (-1,-2) and then back up to (0,0). To go down then back up, we must have obviously intersected an horizontal line twice at any value F(x).

Try it. Draw a graph that goes up and down. Does it pass the Horizontal Line Test? Now, that draw the same graph of F(x) with no lines, and just the points given. Does this pass the Horizontal Line Test?

Of course, the question seems vague, but it also seems like you might have left something out.

Moving down the list of functions. G(x) has value -2 twice. Is this a one-to-one function? Of course not. Whether you draw the graph with lines or just points, it will fail the Horizontal Line Test.

Now, let's find the odd function. I am assuming you know what an odd function looks like on a graph. If not, graph the function f(x)=x.

Starting at F(x). If you are given the point (-2,1), than you must have point (2,-1).
Do you have that point?

I hope I helped out.

Note: I am pretty confident I answered it correctly, if there are mistakes I hope the next guy corrects me, so I can pick up from there.

 

[mathwonk]

"one to one" means no two different inputs give the same output. since the outputs are apparently listed in the rows, "not one to one" means the row which has repeated entries. that would be the second row, for G.

 

[Janitor]

Also, a function that is symmetrical about the origin is an odd function. An odd function is when f(-x)=-f(x).

I agree on your definition of odd function, but I would have said that even functions (such as G in the example above) are the ones best called 'symmetrical.' Anybody?

 

[JasonRox]

Yes, I agree with you Janitor.

To be even more specific one-to-one functions don't have an inverse function, or atleast at the level I am at right now.