End Behavior of a Polynomial Function
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches
positive infinity or negative infinity.
The degree (which comes from the exponent on the leading term) and the
leading coefficient (+ or โ) of a polynomial function determines the end behavior of the graph.
The leading coefficient is significant compared to the other coefficients in the function for the
very large or very small numbers. So, the sign of the leading coefficient is sufficient to predict
the end behavior of the function.
Degree
Leading
Coefficient
End behavior of the function
Graph of the function
Even
Positive
f(x)โ+โ, as xโโโ
f(x)โ+โ, as xโ+โ
Example: f(x)=x^2
Even
Negative
f(x)โโโ, as xโโโ
f(x)โโโ, as xโ+โ
Example: f(x)=โx^2
