We say [math]\text{f:A\longrightarrow B}[/math] is a 1 to 1 function if whenever [math]a,b\in A[/math] and [math]a\ne b[/math] we have [math]f\left(a\right)\ne f\left(b\right)[/math]. The mathematical term 'injective' is also used for these functions.[br]We say [math]f:A\longrightarrow B[/math] is an onto function if the range of [math]f[/math] is equal to [math]B[/math]. The mathematical term 'surjective' is also used for these functions.[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].
Is this function 1-1? Explain your answer.
Are there any intervals for which f(x) is 1-1?
Is this function onto? Explain why.
Now consider the function [math]g(x)=x^4 -x^2[/math] below:
Is this function injective? Explain your answer.
Are there any intervals for which f(x) is injective?
Is this function surjective? 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.
Write down your conjecture here.