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Degree and End Behavior
End Behavior
The end behavior of a graph describes the value of a graph as x approaches positive and negative infinity.
~ Positive infinity ( x -> ∞) goes to the right (x is getting larger).
~ Negative infinity (x -> -∞) goes to the left (x is getting smaller).
The Degree of a Function
The degree of a function is the highest degree of that function.
~ If the degree is even, the function's left and right endpoints are in the same direction. * Both up or both down.
~ If the degree is odd, the function's left and right endpoints are in different directions. * Left side down, right side up
* Left side up, right side down
Max number of turns
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
f(x) = x4 - 3x2 + x + 2
~ The degree of this function is 4.
~ The maximum number of turning points is 3.
Determine a function's end behavior
To determine the end behavior of a function without graphing the function, look at the polynomial's degree and leading coefficient.
~ If the leading coefficient is positive, the right side of the graph will be up.
~ If the leading coefficient is negative, the right side of the graph will be down.
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