Answer:
5. r(x) is f(x) translated down 16 units
7. g(x) is f(x) vertically scaled by a factor of 2/5
Step-by-step explanation:
5. Adding a number to a function value translates that value up by the amount of the number. If the number is negative, the translation is downward. Adding -16 to x^2 translates the graph down 16 units.
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7. Multiplying a function value vertically scales the graph of the function by the multiplying factor. For factors greater than 1, the result is a vertical expansion; for factors less than 1, the result is vertical compression. Here, the function f(x) = x^2 is multiplied by 2/5, so the resulting g(x) is vertically scaled by a factor of 2/5 (compressed).
For a parabola, the effect is to make the graph appear "wider." Values some distance from the line of symmetry that would have been vertically off the page now appear on the page. Hence, the horizontal extent of the graph on the page has increased.
