Question

Match the amplitude, midline, period, and frequency for the cosine equation f(x) = 5cos(2x) + 3.

A) Amplitude = 5, Midline = 2, Period = π, Frequency = 2π.
B) Amplitude = 5, Midline = 3, Period = π, Frequency = 2.
C) Amplitude = 5, Midline = 3, Period = π/2, Frequency = 2.
D) Amplitude = 5, Midline = 3, Period = 2π, Frequency = π.

Answer 1

The amplitude, midline, period, and frequency for the cosine equation are determined based on the equation f(x) = 5cos(2x) + 3. The correct match is Amplitude = 5, Midline = 3, Period = π, Frequency = π.

Step-by-step explanation:

The given cosine equation is f(x) = 5cos(2x) + 3. To find the characteristics of the wave, we analyze the equation:

• The amplitude is the coefficient of the cosine function, so the amplitude is 5.
• The midline is the vertical shift, which is 3 units up, so the midline is y = 3.
• The period is determined by the coefficient of x, which is 2. The period is calculated as 2π/2 = π.
• The frequency is the reciprocal of the period, so the frequency is 1/π or π.

Therefore, the correct match is:

Amplitude = 5, Midline = 3, Period = π, Frequency = π.