How do you determine if #y=3x²+5# is an even or odd function?

Answer 1

#"the function "y =3x^2+5" is even."#

#f(x)=y=3x^2+5#
#if f(-x)=f(x)" then function is even"# #if f(-x)=-f(x)" then function is odd"#
#"so ; "f(-x)=3(-x)^2+5=3x^2+5=f(x)#
#"the function "y =3x^2+5" is even."#
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Answer 2

To determine if a function is even or odd, we need to examine its symmetry properties.

  1. 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.

  2. 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 ):

  1. Test for evenness: ( f(-x) = 3(-x)^2 + 5 = 3x^2 + 5 ) Since ( f(-x) = f(x) ), the function is even.

  2. 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.

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Answer from HIX Tutor

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.

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