Quadratic Functions — Test

Question 9 • Mathematics I

The function f of x is equal to negative x squared minus 2 x plus 15 is shown on the graph. What are the domain and range of the function?

Answer

The domain is start set x such that negative 5 is less than x comma x is less than 3 end set . The range is start set y such that y is less than 16 end set .

The domain is all real numbers. The range is start set y such that y is less than 16 end set .

The domain is start set x such that negative 5 is less than or equal to x comma x is less than or equal to 3 end set . The range is start set y such that y is less than or equal to 16 end set .

The domain is all real numbers. The range is start set y such that y is less than or equal to 16 end set .

Explanation

Complete the square: f(x) = -x² - 2x + 15 = -(x + 1)² + 16. Since (x + 1)² is always nonnegative, the function’s greatest value is 16, which it reaches at x = -1, so the range is y ≤ 16. The quadratic is defined for every real x, so its domain is all real numbers. Choice C gives both.

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