Question

The range of the function \( f(x) = 7\cos(10x + 4\pi) \) is

• A. \( [-1,1] \)
• B. \( [-4\pi, 4\pi] \)
• C. \( [-10,10] \)
• D. \( [-7,7] \)
• E. \( [-2\pi, 2\pi] \)

Hint:

When determining the range of trigonometric functions with coefficients, multiply the standard range by the given coefficient.

Answer 1

The Correct Option is D

Step 1: Understanding the range of the cosine function The standard cosine function, \( \cos(x) \), has a range of: \[ -1 \leq \cos(x) \leq 1. \] Step 2: Scaling by the coefficient 
Given that the function is \( f(x) = 7\cos(10x + 4\pi) \), multiplying the cosine function by 7 scales the range by 7: \[ -7 \leq 7\cos(10x + 4\pi) \leq 7. \] Step 3: Determining the correct range From the above calculation, the range of \( f(x) \) is \( [-7,7] \), which matches option (D).