14
QuizMultiple Choice

Graphing Sine and Cosine — Quiz

Question 14 • Mathematics III

Which of the following is true for f of x is equal to 5 cosine x plus 1 ?

Answer
A
The range of the function is the set of real numbers negative 4 is less than or equal to y comma y is less than or equal to 6 .
B
The period of the function is 10 pi .
C
The function has an amplitude of 2 point 5 .
D
A zero of the function is open paren pi over 2 comma 0 close paren .

Explanation

Cosine ranges from −1 to 1, so 5 cos x ranges from −5 to 5. Adding 1 shifts the range to [−4, 6], making choice A true. At x = π/2, f(x) = 1, not 0; the amplitude is 5 and the period is 2π.

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