Pre-Cal: CSC and SEC graphs

$$y=\csc\left(4\pi x\right)$$  

$$y=\csc\left(4x\right)$$  

$$y=\csc\left(\frac{1}{4}x\right)$$  

$$y=\csc\left(\frac{1}{2}x\right)$$  

Period

Frequency

Max/Min

Amplitude

$$\left[-2,\ 2\right]$$  

$$\left(-2,\ 2\right)$$  

$$\left(-3,\ 3\right)$$

$$\left[-3,\ 3\right]$$  

5

-5

$$\frac{1}{4}$$  

None

2

$$\frac{1}{3}$$  

$$6\pi$$  

-2

down 11

reflection over the x - axis

phase shift = π/2 to the right

period = 1

Amplitude is 6

down 4 units

phase shift = 2π/3 to the right

vertical stretch by a factor of 2

reflection over the x - axis

per = π/3

$\pi$

$2\pi$

$4\pi$

$\frac{3\pi}{2}$

$\frac{\pi}{2}$

$y=\csc\left(x+\frac{\pi}{2}\right)$

$y=\sec\left(x+\frac{\pi}{2}\right)$

$y=\sec\left(x-\frac{\pi}{2}\right)$

$y=\csc\left(x-\frac{\pi}{2}\right)$

All real numbers

All real numbers except odd multiples of π /2

All real numbers except multiples of π

All real numbers between -1 and 1, inclusive; [-1,1]

(-∞, -1] U [1, ∞)