Problem 1 Problem 3Solution1 Period is 4 as graph starts rep

Problem #1

Problem #3

1) Period is 4 as graph starts repeating pattern at x=4

max value = 8 ; min. value = -2

middle point = (8+2)/2 = 5

So, function varies between 5+3 =10 and 3 -5:

Graph represnts phase shifted cosine function:

So, we cn write it as y = 3 +5cos(2pi*x/4) = 3 +5cos(pi*x/2 - pi/2)

x=0 --- y = 3 ; x= 1 ----y = 3+5*1 =8 ; x = -3 ----y = 3 +5cos(pi) = 3-5 = -2

So, the function : y = 3 + 5cos(pi/2(x-1))

2) It may repseresnt a sine function with amplitude =0.7

Period = 2pi/B = pi/4----> B =8

Standard sine function crosses the x axis at x= pi whereas this function crosse x axis at pi/4.

y = 0.7sin(8x)

x=0 ; y =0

x = pi/16 ; y = 0.7sin(8*pi/16) = 0.7

x = pi/8 ; y = 0.7sin(8*pi/8) = 0

x= pi/16+pi/8 = 3pi/16 ; y = 0.7sin(8*3pi /16) = 0.7sin(3pi/2) = -0.7

So, graph repressents: y = 0.7sin(8x)