Consider the following graph of a transformation of a trigon

Consider the following graph of a transformation of a trigonometric function.

(a) Is the function even, odd, or neither even nor odd?

(b) State the period.

(c) Which of the following functions corresponds to the graph?

A. f (x) = – cos(x) – 1

B. f (x) = cos(2x) – 3

C. f (x) = – sin(x) – 2

D. f (x) = sin(2x) – 2

As we see that their is a vertical displacement of -2 units and the given graph is of sine function

Therefore the correct option is

f(x)=-sinx-2

And if f(-x)=f(x then the given function is even. If f(-x)=-f(x),then the given function is odd else it is neither

Lets check out f(-x)

f(-x)=-sin(-x) -2= sinx-2

which is neither equal to f(x) nor to -f(x). Therefore it is neither even nor odd

For period we have to use a sin(bx-c) + d

where period= 2pi/b

we have equation -sinx -2

Here b=1

Therefore period =2pi/1=2pi