Why is the range not all real numbers for this function: f(x)=sin^-1(x)

Question

anonymous · Answer

@ganeshie8 @campbell_st

campbell_st · Answer

the domain is restricted so that it is a function.... 

hence the restriction on the range

anonymous · Answer

wait can you explain in it in a more thorough way

anonymous · Answer

@campbell_st

campbell_st · Answer

well do you know the definition of a function...?

anonymous · Answer

a relationship that involves one or more variables

anonymous · Answer

@campbell_st

campbell_st · Answer

ok... so here is the graph 

|dw:1438027719063:dw|

a simple test for a function is called the vertical line test, hopefully you have know it. 

but a relationship is a function is a vertical line only cuts the curve in 1 place

if you curve us continued

|dw:1438027846892:dw|

the curve when extended to pi and -pi fails the vertical line test so its not a function....