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Give an example of an even function and explain algebraically why it is even.

Mathematics
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So, an even function \(f\) is a function where for all \(x\), \(f(x) = f(-x)\). The square function and the absolute-value functions are pretty cool examples.
is that it?
Maybe.

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Other answers:

Do you know what \(|x|\) is?
x
And \(|-x|\).
x
Bang on!
And do you know what \((-x)^2\) is?
x?
Nope
o
x^2
Yes.
That's correct! =)
so how does that answer this question, bro? :)
You just answered the question, “explain algebraically why it is even”. Look back at the definition.
  • hba
If f(-a)=f(a) then it is even example f(x)=x^2 f(-x)=(-x)^2 f(-x)=x^2 therfore, f(x)=f(-x) @parth explained it well :)
  • hba
:)
Let me do that for an absolute-value function too! So we define the absolute value function as follows\[f(x) = \cases{x \ \ \text{iff} \ \ x >0 \\ -x \ \ \text{iff} \ \ x < 0 }\]It is clear that \(f(-x)=f(x)=x\), hence an even function.

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