Question

Write an equation for the function that is finally graphed after the following transformations are applied to the graph y=|x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis.

Answer 1

FYI- I don't know if the above which is question #2 is part of question #1. #2 really confused me. They are both under graph the function.
#1 was simply to graph the function which I was able to graph it
f(x)= {-x+3 if x<2 and 2x-3 if x>=2

Answer 2

start: y = |x|
shifted right : y = |x-3)
stretched by factor of 3 : y = 3|x-3|
vertically down 2: y = 3|x-3| - 2
reflected about x-axis
y = -3|x-3| + 2

behold the wonders of Wolfram
http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx-3%7C+%2C+y+%3D+3%7Cx-3%7C+%2C+y+%3D+3%7Cx-3%7C+-+2+%2C+y+%3D+-3%7Cx-3%7C+%2B+2

Answer 3

Thanks with you input I was able to do 3, 4, 5, and 6 since they were similar. Could you help me with #7 please.
7) Find the function that is finally graphed after the following transformations are applied to the graph of y = square-root x

Shift up 4 units, reflect about the y-axis, shift right 2 units

Answer 4

y = √x
shift up 4 units -----> y = √x + 4
reflect about the y-axis ---> y = √-x + 4 , for x ≤ 0
shift right 2 units -----> y = √(-(x-2)) + 4 , x≤2

again, Wolfram verifies this

http://www.wolframalpha.com/input/?i=y+%3D+√%28-%28x-2%29%29+%2B+4+from+-10+to+2

I graphed it from -10 to 2