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7 What is the range of the function f(x) = −x² + 60x?

Question 1-7
What is the range of the function f(x) = −x² + 60x?
○ All real numbers that are greater than or equal to 0 and less than or equal to 30
○ All real numbers that are greater than or equal to 0 and less than or equal to 60
○ All real numbers that are greater than or equal to 900
○ All real numbers that are less than or equal to 900

Answer

Question 1-7: All real numbers that are less than or equal to 900 (fourth choice). Completing the square gives f(x) = −(x − 30)² + 900. The maximum value is 900, and the function is unbounded below, so the range is (−∞, 900].

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