The graph of y=csc(x-pi/4)-3 is shown. what is the period of the function? where are the asymptotes of the function? what is the range of the function? y_< ? y_> ? graph

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Prerequisites:

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You need to know

f(x) = A csc⁡(ωx −ϕ)+B

A = Amplitude = |A|

Y-Shift = B

Asymptotes of csc

k = any constant integer number like -3, -2, -1, 0, 1, 2, 3...

Range of csc x

The ranges is from

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Step By Step Explanation:

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Find the Period of the function:

Find the Phase Shift

Find the Asymptotes

We know and when the denominator of is equal to 0, we have an asymptote. So sin = 0 at k*pi .

We know the asymptotes for is where .

The function that is presented has asymptotes at  .+ Phase Shift.

Now, just plugin an integer for k and you will find the asymptotes or you could say the asymptotes are at

Find the range.

We know the range for csc x = . Since we have a Y-Shift of -3, we have to adjust by subtracting -3 from 1 and -1.

1 - 3 = -2

-1 - 3 = -4

New range =  .

2pi, pi/4 + npi, -4, -2

Step-by-step explanation:

Correct on edg assignment

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