Precal Blog

Before we get started, here’s a quick review.  We all know that a graph can be transformed.  It can either be dilated or translated.  Algebraically it would look something like this:  f(x)=a+b(cx-d).  We know that a is a vertical translation, b is a vertical dilation, c is a horizontal dilation, and d is a horizontal translation.  Knowing this, we can transform the graph of Cosine.  The graph of cosine algebraically would look like y=A+Bcos[C(?-D)], where A is a vertical translation, B is a vertical dilation, C is a horizontal dilation, and D is a horizontal translation. The original cosine graph looks like this:

So far, we have only dealt with vertical transformations.  Here are some examples.

y=-2+cos(x)
This graph looks exactly the same as the original cosine graph, just it would be down two.  This means the midline would be at -2 instead of 1.  The amplitude, or how the distance from the critical points to the midline, would still be 1.

y=1/2cos(x)
This graph still has the midline on the x-axis, but it is  just half as tall.  This means that the amplitude would change to 1/2 instead of 1, because the critical points are located at 1/2 and -1/2 instead of 1 and -1.
Another important thing you would need to know is that if cosine is multiplied by a negative number then the graph is flipped around.  So, the pink line represents what the graph would look like if y=-1cos(x).

So, that just about raps it up.  I’m not sure who the next scribe will be because Cammy and Shannon are doing their posts today also.