Question

The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function.

Use the Sine tool to graph the function.

The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

Answer 1

See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1

How to graph the cosine function?

From the question, the given parameters are:

Amplitude, A = 5

Vertical shift, D = -1

Period, T = 4

A cosine function is represented as:

f(x) = A cos(B(x + C)) + D

Where

Amplitude = A

Period = T

Horizontal shift = C

Vertical shift = D

Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0

i.e. C = 0

So, the equation of the cosine function becomes

f(x) = A cos(Bx) + D

Calculate the value of B using

B = 2π/T

So, we have:

B = 2π/4

Evaluate

B = π/2

So, we have:

f(x) = A cos(π/2x) + D

Substitute the known values of A and D in the above equation

f(x) = 5 cos(π/2x) - 1

Next, we plot the graph of the cosine function on a graphing tool

See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1

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