SOLUTION: Could someone help me with this tonight?! Which of the following functions would have even symmetry? y = 2x y = 3x^3 y = 5x^2 + 3 y = 2x

SOLUTION: Could someone help me with this tonight?! Which of the following functions would have even symmetry? y = 2x y = 3x^3 y = 5x^2 + 3 y = 2x - 5 Thank you!

Question 106931: Could someone help me with this tonight?!
Which of the following functions would have even symmetry?
y = 2x
y = 3x^3
y = 5x^2 + 3
y = 2x - 5
Thank you!
Answer by cheesey(22) (Show Source): You can put this solution on YOUR website!
even function are symmetric with respect to y-axis (f(-x) = f(x)). Odd functions are symmetric with respect to origin (f(-x) = -f(x)).
So, take each function a substitute (-x) for x.
y=2x => f(-x) = -2x. Since f(-x) = -f(x) the function is odd.
y = 3x^3 => f(-x) = 3(-x)^3 = -3x^3 is odd
y = 5x^2 + 3 = > 5(-x)^2 + 3 = 5x^2 + 3 and is therefore even function.
y = 2x - 5 => 2(-x) - 5 = -2x - 5 is nether odd nor even since f(-x) does not
equal f(x) or -f(x).
NOTE: Polynomials with all even exponents are even functions; polynomials with all odd exponents are odd functions. However, you should use the f(-x) test when you are not dealing with polynomials.
Hope this helps.
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