Trigonometric Graphs

$$f\left(x\right)=5\sin\left(\frac{1}{2}x+3\right)+2$$  

$$f\left(x\right)=5\sin\left(2x+3\right)+2$$

$$f\left(x\right)=2\sin\left(\frac{1}{4}x+1\right)+5$$

$$f\left(x\right)=4\pi\sin\left(2x+1\right)-7$$

$$\pi$$  

$$2\pi$$  

1

2

$$3\sin\left(2x-\frac{\pi}{3}\right)+9$$  

$$-3\sin\left(4x-\frac{\pi}{6}\right)-9$$  

$$f\left(x\right)=3\sin\left(4x-\frac{2\pi}{3}\right)-9$$  

$$-3\sin\left(4x+\frac{\pi}{6}\right)-9$$  

f(x)=3sin 2x - 1

f(x)=3sin 2x - 1

f(x)=2sin 3x + 1

f(x)=3sin 2x + 1

$$f\left(x\right)=-2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x-\frac{\pi}{6}\right)$$  

$$f\left(x\right)=-2\sin\left(x+\frac{\pi}{6}\right)$$  

$$f\left(x\right)=2\sin\left(x+\frac{\pi}{6}\right)$$  

$$3\pi$$  

$$6\pi$$  

3

6

-1 downwards

$$\frac{\pi}{2}$$  to the left

$$\frac{\pi}{4}$$  to the left

$$\frac{\pi}{4}$$  to the right

$$\frac{\pi}{2}$$  to the right

The function has amplitude -5

The function has a phase shift of $$3\pi$$ to the right

The function has period $$\frac{\pi}{4}$$  

The function has been shifted 4 downwards