Changing k


The following graph shows one case, for k < -1:

For k > -1, the graph still looks like an inverted C:

The bigger k, the 'longer' the graph! Also the 'arms' of the inverted C seems to be 'moving', approaching to -1 as k approaches to -1. This makes sense in contrast with our change of a; when a changes the height of the graph changes. Changing k, we keep fix y but then x changes. The height of the gaphs is always 1.

For k < -1 the behavior is similar, the line x = -1 acts as a mirror, and for smaller values of k the graphs seems to be going more to the left.
Now, what happens when k = -1? Observe that for this case, we get , so we obtain the value x = -1. This explains the 'inversion' of the graphs for k=-1.


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