# What is the end behavior of the graph #f(x)=x^5-2x^2+3#?

To find end behavior, we could always graph and function and see what is happening to the function on either end. But sometimes, we can also predict what will happens.

The general rule for odd degree polynomials is: Positive polynomials: They start "down" on the left end side of the graph, and then start going "up" on the right end side of the graph. Negative polynomials.They start "up" on the left end side of the graph, and then start going "down" on the right end side of the graph.

Let's graph it to check:

graph{x^5-2x^2+3 [-20, 20, -10, 10]}

As you can see, the graph does indeed become infinitely negative of as x gets smaller on the left side, and then becomes infinitely positive as x gets larger on the right side.

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The end behavior of the graph ( f(x) = x^5 - 2x^2 + 3 ) is as follows:

As ( x ) approaches negative infinity, ( f(x) ) approaches negative infinity.

As ( x ) approaches positive infinity, ( f(x) ) approaches positive infinity.

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