M2_8_8_2_2
GeoGebra Construction:
8_2_2
Construct a line and points A, B, and X on the line. Calculate the ratio AX/XB. (GeoGebra will only calculate an unsensed ratio so you will have to supply the sign.) For which points X on AB is this ratio defined? Watch what happens to the ratio as X moves along the line. Use your observations to draw a graph of the function defined by .
Hint: f is a function whose domain consists of the points on AB (excluding B) and whose range consists of real numbers, so your graph should have line AB as its horizontal axis and the real line as its vertical axis.
Solution:
I realized that when all three points are intersecting the ratio is undefined since BX at the moment would be zero. I also notice that when A is between A and B and moves closer to A, the value of the ratio gets closer to 0, when X in on top of A, the ratio is 0 and as it crosses over A it starts to increase. When X is getting closer to B, the ratio starts to increase to the 1000's and then as it passes B it starts to decrease. I could not come up with a graph for this situation.