Question

Given: Graph below - 120 60 30 30 60 90 120 150 180 210 240 270 300 330 360 390 1. State: domain and range x and y intercepts max and min values and where they occur period amplitude axis of symmetry values of a, k, d, and c for the sine function 2. Describe how this graph is related to the base function y=sin x by referring to horizontal and vertical shifts, amplitude, compressions or expansions, reflection.

Answer 1

Own A 300 let tems a sin(kx+ d) + c o state. • Domain Range- Domain Domain go functie chien complete set 8 possible valus Independent variable. Domain 466-00,00) of the a Range The range of function is values (y-values) g all output Range . YE (06) X and y Intercepts- for x intercepts is becauce, not cut by given graph only touch the wo x-axis x- quis. at y=0. CS Scanned with CamScanner

for Y- intercept, at Y-1.5 and Max min and rolus where they Ocaus: мах value - at 2 = 120 by wring Min value o at x=300 graph. . period from X,= -60 X2 : 300, ya Y2:0. da - X, 300- 4-60) = 360. 21 :: Time period : 360° Repeat it self. 1 Amplitude Maxwalue Min-value 6 - 3. • Axis of symmeting X120° Now - sein (Rx+d) +c .. K1 . a= Amplitude = 3, 2 22 a: 3 Time periool 27 CS Scanned with CamScanner

at 2.0, y=115, 1.5 = 3 bin 10+d)+c 15 3 sind to al 2- 180' y = 6 6 3 bin (120° +d)+c. 0 3 bin 120'+) +C = 6 3 sind + c = 1.5 3 sin(100+ d ) - 3 sind = 4.5 sin (180+d) Sind 1.5 is Sin no. cosd + sind.cosiro pug -) 3 cosd + (2) sind pics -) 15 1 he cand 3 sind 2 -> VB = casd pucs es [pucs CS Scanned with CamScanner

ES [ © 60. coso pug.agung [pagi v3 [ cos (d+60) ) = Es 9 cos(d+60 S3 exts cos(+6) ES d+60 = 30 d+10 cos" ( Hood - 30 z us elo from o 3 bin (-30) +c (-) + Зх fc 3 2 - -3=0 = (cest : 3 Sin( x - 30) + 3 Ands CS Scanned with CamScanner

(2) fen) 3 fin ( x - 30) + 3 and general eq. ya binx comparing with then fem): 3 bin (8-36) +3 get right with 30° (raku d) g shifted Y and vertical shift 3 (value of c) left side with rahu af doo, thes, graph shift gry graph shift right dco, then, side d of of with value CPO, then graph shift vertical upward value by the Pop CCO then graph shift vertical downward by yo the value w Here KI means expansions / compression 9. KYL Sin 2 of of compression, espan trien. つくし Ginz sin(2/2) CS Scanned with CamScanner

Amplitude, L. expensien, Son x "grina I sinx an Here Amplitude expansion =3 Au Vertical sheift vertical sheift y = sinat c binx Yo sinx-c w Right shift I left shift (role of d) sina cys sin(a+ 42) CS Scanned with CamScanner