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Answer:
(c) reflection about x-axis, shift right 1
Step-by-step explanation:
The transformation g(x) = p·f(x-h) causes the graph of the function f(x) to be shifted right by h units. It also causes the graph to be vertically scaled by the factor 'p'. When p is negative, the graph is also reflected across the x-axis.
Here, we have p=-2, h=1, so the graph is ...
- reflected across the x-axis
- vertically stretched by a factor of 2
- shifted right 1 unit
This collection of transformations matches the 3rd choice.
_____
Additional comment
The +3 inside parentheses (square brackets) causes the graph to be shifted upward 3 units--before it is reflected and vertically scaled. The reflection across the x-axis causes that upward shift to look like a downward shift, and the vertical stretch causes that shift of 3 units to become a shift of 6 units. (All answer choices agree that the downward shift is 6 units, so we didn't really need to discuss that.)
