(i think the 2 points belong at (-2,0) and blank coordinate between the positive PI symbol and positive 2PI)

Graph the function f(x) = - cos (2x) + 1.

(I think the points belong at (0,0) and (PI,2) )

Using the graphed function above, find the following:

Maximum, Minimum, Period, Frequency, Amplitude, Equation of the midline and Equation of the graphed function.

Termabyte Feb 12, 2020

#1**+2 **

2sin x - 2

This one just makes the sin function twice as "tall" as the normal sine function and shifts it down 2 units

-cos (2x) +1

The 2x makes the period 1/2 as long as the regular cosine graph

The "-" " flips" this over the x axis

The "1" shifts this up one unit

Here's the graph of this : https://www.desmos.com/calculator/wtrtlgunw4

Last one

Max = 1

Min = -3

Period = pi

Frequency = 1 /period = 1/pi

Amplitude = [ Max - Min] / 2 = [ 1 - - 3 ] / 2 = [4] / 2 = 2

Equation of midline.... y = [ Max + Min ] / 2 ......y = [ 1 - 3] / 2 ....y = -2/2 = -1

One possible equation of this function is

y= -2cos(2x) -1

Here]s the graph : https://www.desmos.com/calculator/lk6hffalro

CPhill Feb 12, 2020