Hi, I've been working on this investigation but I do not think I have done the first task very well. The attached image shows the task outline, and the next attached image is a screenshot of 4 different graphs on one which I made to assist in explaining my problem:
I graphed various the function with differing values of n, but I do not really know how to explain what the changes are...
So far I have written the following, but I don't know if it's all relevant and if I can include more...:
For all values of n, the graph line intersects at (1,1).
For 0<n<1, all graphs have asymptotes at x = 0 and y = 0.
As n --> 0, between 0<x<1, the slope becomes more negative and therefore the graph line becomes closer to the y axis near to the origin. Also, as n --> 0, when x > 1, the slope decreases, and therefore becomes closer to the x axis near to the origin.
For n>1, as n increases, the graph lines start moving more towards the y axis near to the origin, and become closer to the x axis near the origin.
If graphs of the function with n = 0.01, 0.1, 1, and 10 are graphed together, obvious conclusions can be drawn.
If 0<n<1, the slope of the function for all x is small, and slowly moves towards its horizontal asymptote of y = 0.
If n>1, the slope of the function for x is relatively large, and particularly for 0<x<1, the slope is large (i.e. more negative).
What can I do to improve my answer by changing it/adding to it/removing from it? Thanks