Question

WILL GIVE MEDAL! FAST! Which of the following is a one-to-one function?

Answer 1

f(x)={5x-1; x<-2}
{ sqrt4(x+2) x>= -2}

Answer 2

f(x)={4;0<=x<2}
{5; 2<=x<4}
{6; 4 <=x<6}

Answer 3

Can you help @zpupster

Answer 4

@ranga

Answer 5

A one-to-one function has a unique x value for every y. If you draw a horizontal line it should intersect the graph at only one point for it to be a one-to-one function.

y = x^2 is NOT a one-to-one function because the graph is a vertical parabola and a horizontal line can intersect the graph in two places.

y = x^3 is a one-to-one function.

f(x) = {5x-1; x<-2} { sqrt4(x+2) x>= -2}
I plotted the graph here: http://www.wolframalpha.com/input/?i=plot+Piecewise [+{{5x+-+1%2C+x+%3C+-2}+%2C+{sqrt%284%28x%2B2%29%29%2C+x+%3E%3D+-2}}+]

If clicking on the link does not work, just copy the entire link (till the closing "]") and paste it into your browser address bar to see the graph.

It is a one-to-one function.

f(x)={4;0<=x<2}
{5; 2<=x<4}
{6; 4 <=x<6}
is NOT a one-to-one function, because same y value of 4 can be x = 0 or 1 or 2.