Question 13 and 14 ! answer and show work : )

Problem 13)

Problem 14)

Step-by-step explanation:

Recall how transformations affect the graph of the sine function, and how such is conveyed into the parameters A, B, C, and D that could be included in the general form of the function:

where the Amplitude of the transformed sine function is the absolute value of the multiplicative parameter A:

Amplitude =

The period is (which for sin(x) is ) is modified by the parameter B in the following manner:

Period =

Where the phase shift is introduced as:

Phase shift = .

and finally any vertical shift is included by the constant D (positive means shift upwards in D many units, and negative means shift downwards D units)

Therefore, to have a sine function with the requested characteristics, we work on the value of the parameters A, B, C, and D one at a time:

1) Amplitude = then we use parameter A = 4

2) Period , then we work on the parameter B:

Period =

which transforms the function into:

3) phase-shift =

Then knowing that B=, we work on the value of parameter C:

Phase shift =

Therefore the function gets transformed into:

4) and finally the vertical shift of negative two units, that gives us the value D = -2

The complete transformed function becomes:

Now for problem 14, recall that the cotangent function is the reciprocal of the tangent function, therefore, their periodicity is the same:

since you are asked for a cotangent function of period as well, there is no multiplication parameter "B" needed (so we keep it unchanged - equal to one). B = 1

Then for the phase-shift which we want it to be , we set the condition:

And insert such in the cotangent general form:

and finally include the desired vertical shift of 2 units: