Question

Find the period, range, phase shift and vertical shift of f(x)=9/2csc(8x+4pi/7)+6

Answer 1

@ganeshie8

Answer 2

Here, on the first page on the bottom they show you how to analyze it into the parameters you're interested in =)
https://www.cedarvalleycollege.edu/FutureStudents/StudentServices/TutoringServices/FAQandResources/Math/Pictures/Transformations%20sec%20and%20csc.pdf

Answer 3

I'm a little confused by that

Answer 4

wait would the period be 2pi/8?

Answer 5

Ok, let's see. they say that if we have
$$
A \cdot \csc(B \cdot x + C) + D
$$Then:
\(|A|\) is our amplitude
\(\frac{2\pi}{B}\) is our period.
\(-\frac{C}{B}\) is our phase shift
\(D\) is our vertical shift and finally
\(-A\) is our X axis flip, which we're not asked here

Answer 6

So yes, the period would be \(\frac{2\pi}{8}\)

Answer 7

what about finding range?

Answer 8

look at the first page on the graph above. you can see that they say Range: \( y \le -1\) or \(y \ge 1\) for csc(x)

Answer 9

if c is 4pi/7 and be is 8 then what would be the phase shift?

Answer 10

b*

Answer 11

Well, \(-\frac{C}{B} = - \frac{ \frac{4\pi}{7}}{8} = -\frac{4\pi}{7 \cdot 8} = -\frac{\pi}{14}\)