Helppp

Is the function y= 7 sin (2x - 3pi/2) even or odd?? How do you figure it out?

 

Hi Lisa, :)

Before I give a specific answer I think it would be a good idea for you to watch this and then you will probably be able to answer your own question.

It is a bit long I know  but if you odd and even really mean it should stick in your brain a whole lot better.

 

https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-introduction-to-symmetry-of-functions/v/recognizing-odd-and-even-functions

 

Basically even functions are symmetrical about the y axis so    f(x)=f(-x)           like y=x^2 is even

so if you reflect the graph across the y axis it will be the same.

 

 

and odd functions have 180 degree rotational symmetry about the point (0,0)    

so so if you reflect the graph across the y axis AND then reflect it acraoo the x axis  it will be the same.   Like y=x^3 is odd

ODD      f(-x)=-f(x)

 

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Is the function y= 7 sin (2x - 3pi/2) even or odd?? How do you figure it out?

 

f(x)=7 sin (2x - 3pi/2)

f(x)=7 [sin (2x) cos(3pi/2)- cos (2x) sin(3pi/2)  ]

f(x)=7 [sin (2x) *0- cos (2x) *-1  ]

f(x)=7 [0+ cos (2x) ]

f(x)=7 cos (2x) 

 

f(-x)=7cos(-2x)

f(-x)=7cos(2x)

f(-x)=f(x)

 

Therefore this is an even function.