Question

I need help making a onto function that is not one to one so far i dont think a parabola will work

Answer 1

@wilsondanielle

Answer 2

I lied i missed the second half of that question

Answer 3

I believe a parabola does work. Now it is up to you to show me why or why not.

Answer 4

let me try something on wolfram

Answer 5

an onto function must use every y value. it doesn't need to pass the horizontal line test like a 1-1 function. Anything that passes the vertical line test would be an onto function.

Answer 6

well a funtion like this f(x) = x^2 should work then

Answer 7

What do you think @inkyvoyd @wilsondanielle

https://www.desmos.com/calculator/lujt1dci93

Answer 8

How about y = x^3 -3x?

Answer 9

that loos good, it is not 1 to 1

Answer 10

y= x(x^2 -3) has 3 roots x =0, \(x=\pm\sqrt3\)
hence the graph looks like

Answer 11

for every y, we have x but it is not one to one. Yeah !!

Answer 12

https://www.desmos.com/calculator/v0vsfb0fxd

Answer 13

a parabola is fine, yes. It won't pass the horizontal line test (so is not 1-1) but it will pass the vertical line test and so will be an onto function.

Answer 14

awesome!

Answer 15

Parabola is ok as long as you limit the range.

Answer 16

next would be for me to find one that is neither onto or 1 to 1 lol f(x) = 0? think that will work?

Answer 17

Like \(f: R\rightarrow [0, \infty) \\x\mapsto x^2\)

Answer 18

that won't work. Pick a function with asymptotes - an onto function is continuous.

Something like tan(x) would work.

Answer 19

so something like f(x)= ceil(x/2)?

Answer 20

oh
i just saw that last part, are you say for neither onto or one to one or just onto?

Answer 21

tan(x) isn't onto, it would technically be 1-1 though as there are no duplicated y values for any given x value

you would need a similar function to get neither onto nor 1-1.

noncontinous = non onto
multiple y values per x = non 1-1

find a function that satisfies both of those requirements.

Answer 22

Parabola works well for not one to one nor onto.

Answer 23

i think i still know the function for a circle...

Answer 24

parabolas are onto.

a circle is x^2+y^2

Answer 25

Like y = x^2 , not one to one for sure
not onto also, since there exist y < 0 in the range but there is no x such that x^2 <0

Answer 26

wouldn't that mean the last answer is not onto?

Answer 27

Parabolas are onto. The requirement for a function to be onto is not a y range from -infinity to infinity, but that every y value IN THE SET is used.

Answer 28

so for the last answer the function y = x^2 would be good

Answer 29

so isf(n)=⌈n/2⌉ onto, or one to one or both?

Answer 30

it is a linear function , so will be both

Answer 31

so x = y^2 wont work either... https://www.desmos.com/calculator/hcx5srg6iy

Answer 32

what about f(x) = 1/x-1 it is a discontinuous @wilsondanielle

Answer 33

nope it wont do

Answer 34

the ceiling function is not one to one.

Answer 35

What about f(x) =2/(x^2-x)

Answer 36

like ceil 3 =3, and ceil 2.6=3 also. Hence it is not one to one

Answer 37

https://www.desmos.com/calculator/cxa3jfeppw

Answer 38

what about that onto is the same as subjective right?

Answer 39

@wilsondanielle

Answer 40

What do you want to find now?

Answer 41

is the last graph i did good for not being one to one or onto?

Answer 42

Actually, It is good since some x's do not have a y. But I am not sure whether it is good to consider it is not onto or not. If they ask, which value of y you don't have preimage? the answer is "infinitive" which is so nonsense to me. :)

Answer 43

lol

Answer 44

If I have y = | x| and I conclude that it is not one to one, since when \(x=\pm 1\), y = 1
It is not onto because if y = -1, I don't have any x such that y = |x|. Very simple and the proof is clear.

Answer 45

ok im still lost, but i just got an idea

Answer 46

why lost?

Answer 47

look at this: http://www.regentsprep.org/regents/math/algtrig/atp5/OntoFunctions.htm

Answer 48

so?

Answer 49

according to that the parabola does not work if it is below 0 or a negetive

Answer 50

hey, look at "WHERE", that is the range. They limit the range to make it onto or not onto.

Answer 51

i just checked it with wolfram it works for the problem

Answer 52

IN example 2, f : R to R, hence it is not onto

Answer 53

even y = x^2 is not onto because it does not include every possble y value

Answer 54

i see

Answer 55

In example 3 f : R to [-2, infinitive), hence it is onto.