Question
Determine whether the following statement is true or false. The minimum value of the function \( y=5 \cos x+4 \) is -1 . Is the statement true or false? True. False, the minimum value is -2 . False, the minimum value is 4 . False, the minimum value is 0 .
Ask by Pena Pollard. in the United States
Feb 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The statement is True.
Solution
The cosine function, cos x, has a range from -1 to 1. Multiplying by 5 and then adding 4 gives:
• Maximum value: 5(1) + 4 = 9
• Minimum value: 5(-1) + 4 = -5 + 4 = -1
Thus, the minimum value of y = 5 cos x + 4 is indeed -1, so the statement is True.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The statement is false; the minimum value of the function \( y = 5 \cos x + 4 \) is actually -1. To find the minimum, we start by recognizing that the cosine function oscillates between -1 and 1. Therefore, substituting the minimum value of cosine into the function gives us \( y = 5(-1) + 4 = -5 + 4 = -1 \). So, the correct answer is: **False, the minimum value is -1.**
