$$g\left(x\right)=2\left(-x-4\right)^2+1$$  

$$g\left(x\right)=-2\left(x+4\right)^2+1$$  

$$g\left(x\right)=-\frac{1}{2}\left(x-4\right)^2+1$$  

$$g\left(x\right)=-2\left(x-4\right)^2+1$$  

Shift the graph of  $$f\left(x\right)$$   2 units to the right

Reflect the graph of  $$f\left(x\right)$$   across the x-axis 

Vertically stretch the graph of $$f\left(x\right)$$  by a factor of 2.

Reflect the graph of  $$f\left(x\right)$$  across the y-axis

Horizontal compression of  $$f\left(x\right)$$   by a factor of  $$\frac{1}{2}$$  .

$$\left|A\right|=3,\ T=4$$  

$$\left|A\right|=\frac{1}{3},\ T=\frac{\pi}{2}$$  

$$\left|A\right|=3,\ T=\frac{\pi}{2}$$  

$$\left|A\right|=\frac{1}{3},\ T=4$$  

$$-2\cos\left(\frac{\pi}{2}x\right)$$

$$2\sin\left(\frac{\pi}{2}x\right)$$

$$-2\sin\left(\pi x\right)$$

$$-2\sin\left(\frac{\pi}{2}x\right)$$

7

-2

3

-3

4π

2π

π

8π

y = 2 cos x

y = sin x

y = 2 sin x

y = sin 2x

y = sin 5x

y = cos 5x

y = 5 sin x

y = 5 cos x

y = -2 cos x - 3

y = 3 cos x - 2

y = -7 cos x - 3

y = -3 cos x - 4

up 2

left 2

right 2

down 2

sine, 2 units up

cosine, 2 units down

cosine, 2 units up

sine, 2 units up

y = 5cos(x - pi) + 3

y = 3cos(x - pi) + 5

y = 3cos(2x - pi) + 5

y = 5cos(2x - pi) + 3

y = -sinθ -1

y = -sinθ/2 -1

y = -2sin2θ + 1

y = sinθ/2 + 1