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How do you determine if #f(x) = 2x^2 - 7# is an even or odd function?

Answer 1

Liam Brennan

It is an even function since #f(-x)=f(x) AA x in RR#

graph{2x^2-7 [-16.02, 16, -8.01, 8.01]}

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Answer 2

Lily Anderson

To determine if the function (f(x) = 2x^2 - 7) is even or odd, you can use the definitions of even and odd functions:

A function (f) is even if (f(-x) = f(x)) for all (x) in the domain of (f).
A function (f) is odd if (f(-x) = -f(x)) for all (x) in the domain of (f).

Apply (f(-x)) to (2x^2 - 7):

[f(-x) = 2(-x)^2 - 7 = 2x^2 - 7]

Since (f(-x) = f(x)), the function (f(x) = 2x^2 - 7) 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.