Question

What are the period, phase shift, and vertical shift of y = csc[3(x + 4)] + 6?

Answer 1

Answer:

Step-by-step explanation:

Alright, lets get started.

The given equation is:

$y= csc [3(x+4)]+6$

$y=csc(3x+12) +6$

Period = $\frac{2\pi }{b}=\frac{2\pi }{3}$

hence the period is = $\frac{2\pi }{3}$

Phase shift = $\frac{-c}{b}=\frac{-12}{3}=-4$

hence phase shift 4 units to the left

ertical shift is 6 units up

So, the answer is C, period 2pi/3, phase shift 4 units left and vertical shift 6 units up  :   Answer

Hope it will help :)

Answer 2

The graph of $y=csc(x)$ is shown in the first picture below

$y=csc(x+4)$
The transformation of adding 4 to the $x$ in $csc(x+4)$ gives the effect of shifting $csc(x)$ four units to the left, as shown in the second picture

$y=csc [3(x+4)]$
The transformation of multiply $csc(x+4)$ by 3 gives the effect of divide $x-coordinate$ by three, as shown in the third picture

$y=csc[3(x+4)]+6$
The transformation of adding 6 to $csc[3(x+4)$ gives the effect of shifting the whole graph by six unit up, as shown in fourth picture

Hence, the correct statement is the first statement
period:pi/3 ; phase shift: 4 units right; vertical shift: 6 units up