Answer:
See the attachment
Step-by-step explanation:
A vertical shift adds a constant to the function value. f(x) ⇒ f(x)+5 is a vertical shift up 5 units.
A horizontal shift subtracts a constant from the independent variable value. f(x) ⇒ f(x-5) is a shift right 5 units.
A multiplying factor of magnitude greater than 1 is a vertical expansion; less than 1 represents a vertical compression. f(x) ⇒ -5f(x) is a vertical expansion (and reflection over the x-axis). f(x) ⇒ (1/2)f(x) is a vertical compression.
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Comment on the vertical compression
You have the function f(x) = x² +2 being transformed to g(x) = (1/2)x² +2. If this were a straight vertical compression, the function g(x) would look like ...
... g(x) = (1/2)(x² +2) = (1/2)x² +1
The fact that the constant has remained +2, instead of being enclosed in parentheses or changing to +1, means that the graph has been compressed vertically around the point (0, 2), not the origin.
