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How do you determine if #g(x) = 4x^2 +2x# is an even or odd function?

Answer 1

Sadie Ackerman

#"neither"#

#• " if "g(x)=g(-x)" then "g(x)" is even"#

#• " if "g(-x)=-g(x)" then "g(x)" is odd"#

#g(-x)=4(-x)^2+2(-x)=4x^2-2x!=g(x)#

#-g(x)=-(4x^2+2x)=-4x^2-2x!=g(-x)#

#g(x)" is neither even nor odd"#

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Answer 2

Liam Brennan

To determine if a function is even or odd, we can analyze its symmetry properties with respect to the y-axis (even functions) or the origin (odd functions).

For a function to be even, it must satisfy the condition: (g(-x) = g(x)) for all (x) in its domain.

For a function to be odd, it must satisfy the condition: (g(-x) = -g(x)) for all (x) in its domain.

Let's apply these conditions to (g(x) = 4x^2 + 2x):

Even function test: [g(-x) = 4(-x)^2 + 2(-x) = 4x^2 - 2x] [g(x) = 4x^2 + 2x]

As (g(-x) = g(x)), the function satisfies the condition for evenness.

Odd function test: [g(-x) = 4(-x)^2 + 2(-x) = 4x^2 - 2x] [g(x) = 4x^2 + 2x]

As (g(-x) \neq -g(x)), the function does not satisfy the condition for oddness.

Therefore, (g(x) = 4x^2 + 2x) is an even function.

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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.