Review+Day+2

In class we discussed the reason why the oscillation of the graph moves when the graph was vertically displaced. Below is the graph of cos(x). As you can see all of the y-coordinates are 1 and -1. So the oscillation is between 1 and -1.



Now let's say that our graph has been vertically displaced by positive 4. So now instead of having the function cos(x) we have the function cos(x)+4. The oscillation of the graph moves when the graph is vertically displaced upwards. It does not stay where the original graph was. It too is shifted upwards by 4. So the oscillation is now between 3 and 5. So the oscillation is also vertically displaced when the graph is vertically displaced. So it "shifts with the graph".

Now what if the graph is stretched horizontally? Does it change where the oscillation at all? Lets say we stretch the graph by 1/3. So the Cos(3x).



Examining the graph and comparing it to the previous graph of Cos(x) we can see that, no, stretching the graph does not effect the oscillation of the graph at all it is still between 1 and -1. So neither vertically displacing the graph or stretching the graph effects the oscillation of the graph.