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How do you determine if #h(x) = 7x^4 -9x^2# is an even or odd function?

Answer 1

Sophie Adams

Because #h(-x)=7*(-x)^4-9*(-x)^2=7*x^4-9x^2=h(x)# where #x# belongs in the domain of #h(x)#
the function is even.

That means that the graph of #h(x)# is symmetric with respect to the y-axis.

Below is the graph of #h(x)# which clearly supports our claim.

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Answer 2

Sadie Alexander

To determine if the function ( h(x) = 7x^4 - 9x^2 ) is even or odd, we evaluate ( h(-x) ) and compare it to ( h(x) ).

If ( h(-x) = h(x) ), then the function is even.

If ( h(-x) = -h(x) ), then the function is odd.

Let's evaluate ( h(-x) ):

[ h(-x) = 7(-x)^4 - 9(-x)^2 ]

[ = 7x^4 - 9x^2 ]

Comparing this with ( h(x) ), we see that ( h(-x) = h(x) ), so the function ( h(x) = 7x^4 - 9x^2 ) is even.

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Answer 3

Liam Brennan

To determine if a function ( h(x) = 7x^4 -9x^2 ) is even or odd, we evaluate ( h(-x) ) and ( h(x) ).

If ( h(-x) = h(x) ), then the function is even.

If ( h(-x) = -h(x) ), then the function is odd.

For ( h(x) = 7x^4 -9x^2 ):

( h(-x) = 7(-x)^4 - 9(-x)^2 = 7x^4 - 9x^2 = h(x) )

Since ( h(-x) = h(x) ), the function ( h(x) = 7x^4 -9x^2 ) is even.

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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.