Combining several transformations The order is very important This power point will demonstrate which order to do them in This will then be applied to a Sine Curve

Y= x2

Y= (2x)2 Horizontal stretch factor ½ HIVO HOVIS Horizontal In side – Horizontal Opposite

Y= (x–3)2 Horizontal translation +3 HIVO HOVIS Horizontal In side – Horizontal Opposite

More Combined Transformations f(x) = (2x – 1)2 f(x) = (x)2 f(x) = (x–1)2 Step 1 Horizontal translation +1

More Combined Transformations f(x) = (2x – 1)2 f(x) = (x–1)2 f(x) = (2x–1)2 Step 2 Horizontal stretch factor ½ All x values are ½ their original value X intercept at x = ½ as expected if 2x–1 = 0 then x = ½

Y= (2x–3)2 Horizontal translation +3 Horizontal stretch factor ½

So the order is: Translate horizontally left or right Stretch horizontally Stretch Vertically Translate vertically HIVO Horizontal Inside Vertical Outside HOVIS Horizontal Opposite Vertical Is Same

We need to sketch the graph of y = 3sin(5t+90)+2 Trig Transformations y y=sint t jhvjvjvh We need to sketch the graph of y = 3sin(5t+90)+2

Trig Transformations y period = 360 y=sint t Crosses x axis at 0, 180, 360, 540

Trig Transformations y y=sin(t+90) Translate horizontally left or right t Horizontal translation of -90 Inside = horizontal opposite Crosses x axis at 90, 270, 450

Trig Transformations y Wave frequency = 5 Period = = 72 y=sin(5t+90) 72 t Stretch horizontally Horizontal stretch of  Inside = horizontal opposite Crosses x axis at 18, 54, 90

Trig Transformations y Stretch Vertically y=3sin(5t+90) t Vertical stretch of factor 3 Outside = vertical same

Trig Transformations y y=3sin(5t+90)+2 t +2 Vertical translation of +2 Outside = vertical same

Sketch the graph of y = 1sin(t + 45) y = 2sin(t + 30) y = 3sin(2t – 90) y = 4sin(3t + 60)

y = 1sin(t + 45) y = 2sin(t + 30) 1 2 y = 3sin(2t – 90) Translate horizontally by –30 Stretch vertically factor of 2 Translate horizontally by –45 y = 3sin(2t – 90) y = 4sin(3t + 60) 3 4 Translate horizontally by +90 Stretch horizontally by ½ Stretch vertically factor of 3 Translate by horizontally –60 Stretch horizontally by 1/3 Stretch vertically factor of 4