Question

Are any of these one-to-one functions?

let f:{a,b,c,d}→{a,b,c,d} be given by

1.
f(a)=b
f(b)=a
f(c)=c
f(d)=d

2.
f(a)=b
f(b)=b
f(c)=d
f(d)=c

3.
f(a)=d
f(b)=b
f(c)=c
f(d)=d

Is this next function onto?:

Let f:{a,b,c,d}→{a,b,c,d}f:{a,b,c,d}→{a,b,c,d} be given by

4.
f(a)=bf(a)=b
f(b)=af(b)=a
f(c)=cf(c)=c
f(d)=df(d)=d

Answer 1

Start with the definition of a one-to-one function. Do you know what it is, and what the requirements are?

Answer 2

every x has a unique value so like (a,c)

Answer 3

That's the requirement for a function (it passes the vertical line test). If it's a 1-1 function, it also has to pass the horizontal line test - no y values are repeated either.

So, for example #3 has d on there twice - once for f(a) and once for f(d). Therefore, it is not a 1-1 function.

Answer 4

the same for 2

Answer 5

Correct. what about 1?

Answer 6

i dont think so i keep getting something like a parabola

Answer 7

@wilsondanielle

Answer 8

i gave A - D values and graphed them a = 1 b = 2 c=3 d=4

Answer 9

I would argue that it would be, as you don't know the values of any of them and neither of them repeat.

Answer 10

what about number 4?
f(a)=b
f(b)=a
f(c)=c
f(d)=d

the onto means every y value was used.

Answer 11

so i would say number 4 is onto @wilsondanielle

Answer 12

I believe so, because again neither x nor y values repeat.

Answer 13

ok, thank you