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For these functions, determine which ones are EVEN. (y axis symmetry)  a) f(x)=3x^4 +...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted June 14, 2013 at 11:41 PM via web

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For these functions, determine which ones are EVEN. (y axis symmetry) 

a) f(x)=3x^4 + 4

b) f(x) = x^3 + 4

c) f(x) = x^2 + x - 3

d) f(x) = 2x^4 + x^2 + 1

e) f(x) = 4

f) f(x) = x^4 + x^3 + x^2 + x + 1

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ishpiro | Teacher | (Level 2) Associate Educator

Posted June 14, 2013 at 11:50 PM (Answer #1)

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Functions a, d, and e are even because they contain only even powers of x (or no x at all, as in e).

By definition, even function obeys the condition

f(-x) = f(x).

For any even power n of x

`(-x)^n = x^n`

So the functions that contain only even powers of x are even.

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crawfordcomeaux | eNotes Newbie

Posted June 14, 2013 at 11:56 PM (Answer #2)

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A, D, E

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