Below is the graph of y = acos(bx+c)+d, where a, b, and c are positive, and c is as small as possible. Find a + b + c+d.
The graph of cos is shifted up (by d) , shifted RIGHT (to make c as small as possible ----- c will be NEGATIVE) and amplified (by a) and period is increased to 3pi (from normal 2pi)
Amplification 'a' Normal cosine is from -1 to 1 ( amplitude = 1) this graph is from -1 to 3 (amplitude = 2) so a = 2
Period is changed by b = 2/3
shifted LEFT by 3pi/2 (to make c as small as possible, but still positive) but multiplied by 2/3 (above) makes it just pi pi = c
And finally ....shifted UP from midline = 0 to midline = 1 1 = d
Here is a graph:
( RED text is edited/corrected text....THANX to CPhil !)