Question

G(x) = 2 cos [2x (x+2π/3)] -5 With respect to the parent function F(x) = cos(x) What is the amplitude, period, phase shift, and vertical translation of the function G(x)?

Answer 1

The amplitude is 2

The period is π/x

The phase shift is -2π/3

The vertical translation is -5

Explanation:

The equation of the given function is G(x) = 2·cos[2·x·(x + 2π/3)] - 5

Comparing with the general equation for the cosine function, y = d + a·cos(b·(x - c))

Where:

`\left | a \right |` = The amplitude

2·π/b = The period

c = The phase shift

d = Vertical shift

Therefore, we have;

The amplitude = 2

The period = 2·π/(2·x) = π/x

The phase shift = -2π/3 (The sign is opposite to in sign to the sign following it in the parenthesis of the angle of rotation

-5 = The vertical translation of the function G(x)