1. Graph the function f(x)=2 sin x-2 (Graph 1)

2. Graph the function f(x)= - cos (2x) + 1 (Graph 2)

Explanation:

The function is

To plot the function in the graph, first we shall determine the amplitude, period, phase shift and vertical shift.

The function is of the form,

where A is the amplitude =

Period is ,

Phase shift is C,

Vertical shift is D.

Hence, from the function , we have,

Amplitude =

Period =

Phase shift = 0

Vertical shift = -2

Now, substituting the values for x, we get the corresponding values for y.

For ⇒

For ⇒

For ⇒

For ⇒

For ⇒

Hence, plotting these points we get the graph which is attached below:

Now, we shall graph the function

Similarly, we shall determine the amplitude, period, phase shift and vertical shift.

Amplitude =

Period =

Phase shift = 0

Vertical shift = 1

Now, substituting the values for x, we get the corresponding values for y in the function

For ⇒

For ⇒

For ⇒

For ⇒

For ⇒

Hence, plotting these points we get the graph which is attached below:

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