How do you determine if #y=3x²+5# is an even or odd function?
By signing up, you agree to our Terms of Service and Privacy Policy
To determine if a function is even or odd, we need to examine its symmetry properties.
-
Even function: A function ( f(x) ) is even if ( f(-x) = f(x) ) for all ( x ) in the domain. In other words, if replacing ( x ) with ( -x ) does not change the function's value.
-
Odd function: A function ( f(x) ) is odd if ( f(-x) = -f(x) ) for all ( x ) in the domain. In other words, if replacing ( x ) with ( -x ) results in the negative of the function's value.
For the function ( y = 3x^2 + 5 ):
-
Test for evenness: ( f(-x) = 3(-x)^2 + 5 = 3x^2 + 5 ) Since ( f(-x) = f(x) ), the function is even.
-
Test for oddness: ( f(-x) = 3(-x)^2 + 5 = 3x^2 + 5 ) ( -f(x) = - (3x^2 + 5) = -3x^2 - 5 ) Since ( f(-x) \neq -f(x) ), the function is not odd.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7