Question

In: Advanced Math

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.

Expert Solution

A graph of y = Acsc(Bx – C) + D shows following features:

The stretching factor is |A|

The period is P = 2π/|B|.

The domain is all real numbers x, where x ≠ C/B + π/2|B|k, k is an integer

The range is (-∞, -|A|] ∪ [|A|, ∞).

The asymptote occurs at x = C/B + π/2|B|k

The equation for midline is y = D

There is no amplitude.

It is an odd function.

Consider the following function:

f(x) = 2csc(x + π/4) - 3

Since y = Acsc(Bx – C) + D does not have any amplitude.

So, the function f(x) = 2csc(x + π/4) - 3 has no amplitude.

Since B=1, therefore the period is as follows:

P = 2π/|B|

= 2π/1

= 2π

Since D = -3, therefore the equation for midline is as follows:

y = D

y = -3

Now use maple to draw the graph of above function as follows:

Junaid answered 1 year ago

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