# How do you determine if # x / (x^2 + 5)# is an even or odd function?

Definitions

even operate

strange operation

Is it even?

Is this strange?

From the graphic representation, graph{x/(x^2+5) [-1.758, 2.57, -1.031, 1.13]}, we can observe that the graph is odd because it is reflected through the origin and not in the Y-axis.

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To determine if ( \frac{x}{x^2 + 5} ) is an even or odd function, we evaluate the function at ( -x ) and compare it to the original function.

For an even function, ( f(-x) = f(x) ). For an odd function, ( f(-x) = -f(x) ).

If ( \frac{x}{x^2 + 5} ) is even, then ( \frac{-x}{(-x)^2 + 5} ) should equal ( \frac{x}{x^2 + 5} ). If ( \frac{x}{x^2 + 5} ) is odd, then ( \frac{-x}{(-x)^2 + 5} ) should equal ( -\frac{x}{x^2 + 5} ).

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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.

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.

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.

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