The graph of the function f(x) = –(x + 3)(x – 1) is shown below.
What is true about the domain and range of the function?
A). The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1.
B). The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4.
C). The domain is all real numbers, and the range is all real numbers less than or equal to 4.
D). The domain is all real numbers less than or equal to 4, and the range is all real numbers.
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Answers
Given : The graph of the function f(x) = –(x + 3)(x – 1) is shown below.
To Find : What is true about the domain and range of the function?
A). The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1.
B). The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4.
C). The domain is all real numbers, and the range is all real numbers less than or equal to 4.
D). The domain is all real numbers less than or equal to 4, and the range is all real numbers.
Solution :
C). The domain is all real numbers, and the range is all real numbers less than or equal to 4.
f(x) = –(x + 3)(x – 1)
Passes through ( 1, 0) and (-3 , 0)
-(x² + 2x - 3)
=-((x+ 1)² -4)
= 4 - (x+ 1)²
=> f(x) ≤ 4
Hence Range ≤ 4
C). The domain is all real numbers, and the range is all real numbers less than or equal to 4.
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