These values of determine the of the coordinates of the five key points for x x-coordinates five key points on the graph. To obtain the y- , we coordinates of the five key points for the y- 1 sin ⎞ + 3 x = − y π ⎛ ⎛ π ⎞ + 3 cos 1 , we multiply the y x y- 2 ⎝ 8 ⎠ ⎜ ⎟ 2 ⎝ 4 ⎠ 2 coordinates of the five key points for = sin y x coordinates of the five key points for = cos 1 3 y x by by = − and then units. Thus, the A A unit. Thus, the 2 add 3 and then add 1 2 2 2 1 π ⎛ ⎞ 3 sin ⎜ ⎟ + graph of x y graph of will lie between will lie between = − y 2 8 2 π 3 cos ⎛ ⎞ + 1 x =− ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ 2 4 2 1 and 2 on the The five key points are y-axis. −1 and 2 on the The five key points are y-axis. ⎛ 3 ⎞ ⎛ ⎞ 3 ⎛ ⎞ 3 (0, (4, (8, −1) ⎛ ⎞ ⎛ ⎞ , 2, 1 , 2) , 6, 1 , (4,1) (12, −1) ⎜ 0, 2 ⎟ , , ⎜ 8, 2 ⎟ , 2) , ⎜16, 2 ⎟ ⎜ 2 ⎟ ⎜ 2 ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below. We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below.
These values of x determine the x-coordinates of the five key points on the graph. To obtain the y- coordinates of the five key points for coordinates of the five key points for y = − 1 sin ⎛ π x ⎞ + 3 , we the y- y 3 cos ⎛ π x ⎞ + 1 , we multiply the y- 2 ⎝ 8 ⎠ ⎜ ⎟ 2 ⎝ 4 ⎠ 2 coordinates of the five key points for y = sin x coordinates of the five key points for y = cos x 1 3 by A 3 and then add 1 unit. Thus, the by A = − and then add 2 units. Thus, the 2 2 2 1 ⎛ π ⎞ 3 graph of y 3 cos ⎛ π x ⎞ + 1 will lie between graph of y = − sin ⎜ x ⎟ + 2 8 2 will lie between =− ⎜ ⎟ ⎝ ⎠ 2 ⎝ 4 ⎠ 2 1 and 2 on the y-axis. The five key points are −1 and 2 on the y-axis. The five key points are ⎛ 3 ⎞ ⎛ 3 ⎞ ⎛ 3 ⎞ (0, −1) , ⎛ 2, 1 ⎞ , (4, 2) , ⎛ 6, 1 ⎞ , (8, −1) ⎜ 0, 2 ⎟ , (4,1) , ⎜ 8, 2 ⎟ , (12, 2) , ⎜16, 2 ⎟ ⎜ 2 ⎟ ⎜ 2 ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below. We plot these five points and fill in the graph of the curve. We then extend the graph in either direction to obtain the graph shown below.
62514-0132318806_ISM_02-1.docx