Question

Can someone please help me understand how to graph y=3cos(x/4)-5

Answer 1

draw your standard cos(x) function, with tics at standard places: 0,pi/6,pi/4,pi/3,pi/2,pi, etc.

Now, you want x/4 to be those values, instead of x. So, multiply all the x-values by 4: change the labels to
0,2pi/3,pi,4pi/3, ...
Now you have a graph of cos(x/4)

Relabel the y-axis to go from -3 to 3 instead of -1 to 1.
Now you have a graph of 3cos(x/4)

Now Relabel the y-axis by subtracting 5 from what it shows, so it now runs from -8 to -2

Draw a new x-axis at the new y=0, and you have a graph of 3cos(x/4)-5