Question

 Provide an example of a trig function and describe how it is transformed 
from the standard trig function f(x) = sin x, f(x) = cos x, or f(x) = tan x 
using key features.

Answer 1

It's not 100% clear what you're asking for here.

If you begin with f(x) = sin x, and write the new function g(x) = sin (x-pi/2), you get 

g(x) = sin x cos pi/2 - cos x sin pi/2  =  -cos x 

This has a graph obtainable by shifting the graph of sin x pi/2 units to the right.

h(x) = sin (x+pi/2) has a graph obtainable by shifting the graph of sin x pi/2 units to the left.