NEED ANSWERED ASAP Graph the following Trigonometric Function

Question

f(x)= 4cos(2x)-1 on the interval [0,3π]

 

 

State:
amplitude
phase shift

period

equation of axis

domain

range

 

 

What would be my mapping rule for this and the points on my graph?

Answer 1

f(x)= 4cos(2x)-1 on the interval [0,3π]

 

 

The general form for a cosine function is f(x) = Acos[B(x - C)] + D.

 

 

|A| is the amplitude.

 

B is the angular frequency.  The period is 2π/B.

 

C is the horizontal shift.  (The phase shift is C or BC depending on who you ask, so ask your teacher.)

 

D is the vertical shift.

 

 

f(x)= 4cos(2x) - 1:

 

 

|A| = 4 for the amplitude

 

B = 2, so period is 2π/2 = π.

 

C = 0, so the phase shift is zero.

 

D = -1, so the axis of the cosine function is y = -1.

 

 

The domain is restricted in the interval, [0,3π].

 

The range is [-5,3] since the maximum distance away from y = -1 is 4 units on both sides.

 

 

To graph your trig function, try https://www.desmos.com/calculator.  Good luck!