HELP HELP HELP

Huge thank you to both of you guys for taking the time to help!

-3  determines the amplitude      cos goes from -1 to 1    the subtract one at the end of the equation shift the graph DOWN  1

-3  to 3      then shift down ONE   -4  to  2 is the min  and max

(2(x-pi/4)    

  the 2   will increase the frequency by a factor of 2    the pi/4 will shift the graph to the right (.785398 radians)

(I think)

I am not  ABSOLUTELY positive of these answers...I saw this question was not answered yesterday, so I took a stab at it today.

If you go to desmos graphing calculator , you can confirm all of this !   

Anyone else?

Thanks ElecteicPavlov  , I will take a look independently of you :)

WHAT IS THE MAXIMUM AND MINIMUM OF y=-3cos(2(x - pi/4))-1 and how to graph this function on paper??

The -3 means that the amplitude, distance from the centre, is |-3|=3 

so

y=-3cos(2(x - pi/4))     would go from y=-3 to y=3

BUT the -1 at the end drops the graph by 1 unity so the y values will go from   -4 to 2

------

What about the x values ??

Consider y=cosx    this has a period (wavelength)   of 2pi,  and max y=+1 miny=-1

The maximums are at  x=0, x=2pi,  x=2npi where n is an integer.

The minimums are half way inbetween,   x=pi, x=3pi  etcThe 

now look at

----------------------------------------------

y=cos(2x)

The period is now  2pi/2 = pi

so

The maximums are at  x=0, x=pi,  x=npi where n is an integer.

The minimums are half way inbetween,   x=pi/2, x=3pi/2  etc

But there is also a phase shift.  The -pi/4 moves the graph pi/4 places in the positive direction

so

The maximums are at  x=0+pi/4, x=pi+pi/4,  x=npi where n is an integer.

That is  x=pi/4,  5pi/4 etc

The minimums are half way inbetween,   x=pi/2+pi/4, x=3pi/2+pi/4  etc

That is  x= 3pi/4,  x=7pi/4 etc

so we have Maximums,    (pi/4, 2),  (5pi/4,2)    etc

and the minimums are      (3pi/4,-4)  (7pi/4,2)   

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Oh, I almost forgot about the NEGATIVE sign at the front.  That turns the whole graph upside down.  I mean it reflects it about y=0 which is the x axis.  but that was BEFORE we dropped the whole graph by -1.

so

so we have MINIMUMS,    (pi/4, -4),  (5pi/4,-4)    etc

and the MAXIMUMS are      (3pi/4,2)  (7pi/4,2)    etc

This is displayed better in the interactive graph below.  Make sure you look at it and learn all that you can from it.

You have to click into the site.

Lets see how I would have 'grown' this graph.

Click the buttons down the side to show the graphs one by one ans you will see how I have 'built' the graph from the basic starting point of   y=cosx

https://www.desmos.com/calculator/swwpidnui6