End behavior refers to the direction the graph of a function approaches as the input (x-values) approaches positive infinity or negative infinity.
For example, let's consider the function f(x) = 2x^3 - 5x^2 + 3x - 2.
To analyze the end behavior of this function, we can look at the leading term, which is 2x^3.
As x approaches positive infinity, the leading term becomes larger and larger positive values dominate. Therefore, the graph of the function will also approach positive infinity.
As x approaches negative infinity, the leading term becomes larger and larger negative values dominate. Therefore, the graph of the function will approach negative infinity.
In conclusion, the end behavior of the graph of the function f(x) = 2x^3 - 5x^2 + 3x - 2 is that it approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity.
End Behavior in graph example
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