SOLUTION: Are the four listed functions even or odd? f(x)=0 f(x)=-x+2 f(x)={|x| if x<0 and x^2 if x > or equal to 0} f(x)=4x^94 Thank you.

Algebra ->  Functions -> SOLUTION: Are the four listed functions even or odd? f(x)=0 f(x)=-x+2 f(x)={|x| if x<0 and x^2 if x > or equal to 0} f(x)=4x^94 Thank you.      Log On


   

Question 44841: Are the four listed functions even or odd?
f(x)=0
f(x)=-x+2
f(x)={|x| if x<0 and x^2 if x > or equal to 0}
f(x)=4x^94
Thank you.
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
An even function is symmetric about the y-axis, and an odd function is not symetric.
First of all, f(x)=0 is even. any value of x, whether it is >0 or <0, will give the same result. It is symmetric about the y-axis.
Now let's plot the functions (y=f(x)):
f(x)=-x+2 is red
f(x)=|x| is green
f(x)=4x^94 is blue
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-x%2B2%2C+sqrt%28x%5E2%29%2C+4x%5E94+%29+
From the graph you can see that
f(x)=|x| and f(x)=4x^94 are even,
and f(x)=-x+2 is odd.
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam