Where does a cosine graph with an "a" value =/= 1 start?

Question

The function for a cosine graph is f(x)=a cos b (x-c) + d, and in the parent function of f(x)=cos x, the "a" value = 1. I was taught that in a cosine function the graph "starts" at (0, 1). Is this also true when a does NOT = 1? Does the cosine graph really start at (0, "a")? 

 

Thank you!

Answer 1

Mel, the simple answer to your question is yes. 

 

y = 2cosx would start at (0,2) and y = -5cosx would start at (0,-5) and be upside down.

 

You will learn about vertical and horizontal shifts, which will affect this somewhat. With a vertical shift of 2 and a = 3, it would start at (0,5).

 

Hope this makes sense!