Parent function question

So the parent function basically means the simplest mathematical equation to represent a curve. 

In this case its a sine curve. Now if you were to replace x with 2x, physically you are increasing the frequrency of the curve and by using the scalar -3 you are scaling and limiting it to the amplitude range of +3 and -3 instead of -1 to 1. This basically implies that the form remains the same in all cases as they all belong to the same family of cosine curves. 

for better understanding: 

http://fooplot.com/

Plot your cosine functions to see the change!

\(y = cos(x) \)

The parent function is the simplest form of the given function with the same degree.

So it wouldnt be y= -3 cos 2x ??

What is the parent function of y= -3 cos (2(x - pi/4))-1 

I am not so sure about this parent function term.  I am not at all sure that there is a definative answer.

If I was going to 'grow' this graph I would do it in this order.

1) cos(x)                             

2) cos(x-pi/4)                 graph moved pi/4 units to the right         

3) cos(2(x-pi/4))             Graph wavelength halved   (now pi units)

4) -cos(2(x-pi/4))            Graph turned upside down - reflected across the y=0

5) -3cos(2(x-pi/4))          amplitude increased from 1 to 3

6) -3cos(2(x-pi/4))-1       whole graph dropped one unit.

4 and 5 could be done in either order or both together.

So my lay use of the term would call all of the ealier functions parent functions....

Here is how I could build the graph.

Click on the circles at the side of the graph one at a time to see what is happening.

I know this is not much of an answer, I just thought you mjight find it interesting or helpful.

https://www.desmos.com/calculator/3sguge1npe