The graph that correctly represents this cosine function f(x) = 2cos(3x) is: B. graph B.
In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
- A represents the amplitude.
- B = 2π/P.
- P represents the period.
- C represents the phase shift.
- D represents the center line (midline).
Generally speaking, a cos(θ) function has a maximum value of 1 at θ = 0 and θ = 2π, and a minimum of value of -1 at θ = π. Also, its x-intercepts are at θ = π/2 and θ = 3π/2.
In order to determine the graph that represents the given cosine function, we would have to determine the y-intercept (where the graph cuts the x-axis when x is 0);
f(x) = 2cos(3x)
f(0) = 2cos(3(0))
f(0) = 2(1)
f(0) = 2
Therefore, the y-intercept is (0, 2) as correctly depicted by graph B only.
Complete Question;
Choose the graph of the following function f(x)=2cos(3x)