Is Sin(x) a 1:1 Function and What Defines a Function?

[Chadlee88]

Is the following correct.

1. f(x) is a function if for every x value there is exactly one y value. so sin x is a function.

2. does a 1-1 function mean that the line y = constant cut the graph in exactly one place? therefore sin (x) is not a 1:1 function but is still a function?

 

[Random333]

Is the following correct.

1. f(x) is a function if for every x value there is exactly one y value. so sin x is a function.

2. does a 1-1 function mean that the line y = constant cut the graph in exactly one place? therefore sin (x) is not a 1:1 function but is still a function?

Yes that is correct.

$$\\sin x$$ is a function that is a many to one function. That is there are multiple x values that give the same value as y or f(x). For example if you sub in $$x={\pi}/{2}$$ and $$x={5\pi}/{2}$$ into $$y= \\sin x$$ you get y=1 in both cases.

Thus you have a many to one function. There is also a many to many graph which obviously isn't a function due to the vertical line test.

 

[Muzza]

Number 2 is not correct. A function (from R to R) is injective if and only if the line y = constant cuts the graph in AT MOST one place.