Answer:
see attached
Explanation:
You want a graph of the given piecewise function f(x) after it has been transformed to -3f(3/2x) +2.
Transformations
The various transformations that can be applied to a function are ...
g(x) = a·f(b(x-c)) +d
where ...
- a = vertical expansion factor; negative values reflect the graph over the x-axis
- b = horizontal compression factor; negative values reflect the graph over the y-axis
- c = horizontal translation to the right
- d = vertical translation up
Application
Comparing this form to the given function, we see ...
- a = -3: expanded vertically by a factor of 3 and reflected over the x-axis
- b = 3/2: compressed to by a factor of 3/2 to 2/3 the original width with respect to the y-axis. (Each x-coordinate is multiplied by 2/3 to give the x-coordinate of the scaled graph.)
- c = 0: no horizontal translation. (The apparent right shift in the vertex is a result of the horizontal compression.)
- d = 2: translation of the vertically reflected graph upward 2 units
The scaled and shifted graph is the green graph shown in the attachment.