Final answer:
The question discusses transforming a function with vertical translation, horizontal compression, and vertical stretch, as well as plotting a linear equation by creating a table of values and graphing them.
Step-by-step explanation:
The question provided involves transformations of functions, which is a mathematical concept typically covered in high school curriculum. The functions given (I)y=f(x)-2, (II)y=f(2x), and (III)y=3f(x) represent vertical translations, horizontal compressions, and vertical stretches of the base function f(x), respectively. To understand these transformations, one can consider how the graph of the base function is altered: vertically shifting by 2 units down, horizontally compressing by a factor of 1/2; and vertically stretching by a factor of 3.
In the case of y = 9 + 3x, we have a linear equation where 9 is the y-intercept and 3 is the slope of the line. The process of creating a table of values involves selecting different x coordinates, substituting them into the equation, calculating the corresponding y values, and plotting these points on a graph to form a straight line.