If you're is supposed to graph y=2^x and then stetch it vertically by factor 1.29 units and then shift it -2.61 units, how would you write that as an equation? y=(2-1.29)^x-2.61, is that correct?
To stretch vertically by factor 1.29 you multiply y values by 1.29. This would change the basic function
y = 2^x
to the function
y = 1.29 * 2^x.
Assuming the shift is horizontal, i.e., in the x direction, you would then replace x by x - h with h = -2.61. Thus x would be replaced by x - ( - 2.61) = x + 2.61 and your function would become
y = 1.29 * 2^(x + 2.61).
When it says to find the average rate of depth change during each of the 3 time intervals, does that mean to find each change between each interval or as a whole?
The key word is 'each'. The statement is to 'find the average rate of depth change during each of the 3 time intervals', so you find each. That is, you find 3 different average rates.
This is an error made by many students on Major Quizzes and I'm glad you asked.
If it says 'If f(x)=x^2, then what are : f(x-.75), f(x)=-.75, etc...' then do you just plug in
Right. You get
f(x - .75) = (x - .75)^2 and
f(x) - .75 = x^2 - .75.