A 1 to 1 function is where every x is mapped to a unique value of y, the mathematical term is injective[br]An onto function is where every y is mapped from at least one x value, mathematical term is surjective.[br][br]On the following graph, adjust the values of [math]a[/math] to move the line [math]y=a[/math] and find points of intersection between the line and the function [math]f(x)[/math].[br][br]1) Is this function 1-1? Explain your answer.[br]2) Are there any intervals for which [math]f(x)[/math] is 1-1?[br]3) Is this function onto? Explain why.

What about the function [math]g(x)=x^4 -x^2[/math] below:[br]1) Is [math]g(x)[/math] 1-1?[br]2) Are there any intervals for which [math]g(x)[/math] is 1-1?[br]3) Is this function onto? Explain why.

What features should a graph have in order to represent a 1-1 function? What about an onto function? Test your conjectures by entering a function in the graph below and applying the appropriate tests.