Question

what is the amplitude of this function $f(x)$?
$f(x) = 3cos(2x) + 5$
enter your answer in the box.

Explanation:

Step1: Recall the general form of a cosine function

The general form of a cosine function is \( f(x) = A\cos(Bx - C) + D \), where \( |A| \) is the amplitude, \( \frac{2\pi}{|B|} \) is the period, \( \frac{C}{B} \) is the phase shift, and \( D \) is the vertical shift.

Step2: Identify the value of \( A \) in the given function

In the function \( f(x) = 3\cos(2x) + 5 \), comparing it with the general form, we can see that \( A = 3 \).

Step3: Determine the amplitude

The amplitude is the absolute value of \( A \). Since \( A = 3 \), the amplitude is \( |3| = 3 \).

Answer:

3