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Classify each function as even, odd, or neither even nor odd.

Drag the choices into the boxes to correctly complete the table.



(SEE PICTURE)

Classify each function as even odd or neither even nor odd Drag the choices into the boxes to correctly complete the table SEE PICTURE class=

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remotecontrolbrain

The function

f(x) is even

g(x) is neither even nor odd

h(x) is odd

Steps:

for an even function it holds that f(-x) = f(x):

f(-x) = (-1)^6 x^6  - (-1)^4 x^ 4 = x^6 - x^4 = f(x) => f is even

for an odd h(x) it holds that h(-x) = -h(x):

[tex]h(-x) = (-1)^5x^5-(-1)^3x^3 = -(x^5-x^3) = -h(x) \implies h(x)\,\, \mbox{even}[/tex]

It is easy to show that g(x) does not match any of the two possibilities above.


Answer: f(x) is an even function, g(x) is neither odd nor even and h(x) is an odd function.

Step-by-step explanation:

Since we have given that

[tex]f(x)=x^6-x^4[/tex]

We will check it for even or odd:

Consider ,

[tex]f(-x)=(-x)^6-(-x)^4=x^6-x^4=f(x)[/tex]

So, it is even function.

[tex]g(x)=x^5-x^4\\\\g(-x)=(-x)^5-(-x)^4=-x^5-x^4\neq g(x)[/tex]

So, g(x) is neither even nor odd.

[tex]h(x)=x^5-x^3\\\\h(-x)=(-x)^5-(-x)^3=-x^5+x^3=-(x^5-x^3)=-h(x)[/tex]

so, it is odd function.

Hence, f(x) is an even function, g(x) is neither odd nor even and h(x) is an odd function.

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