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Lesson 5

Definitions Associated With Graphing Polynomial Functions

TermDefinition
Zero of a Function The point at which the graph of a polynomial touches or crosses the x-axis, also known as x-intercepts
Multiplicity The number of times that a zero's associated factor appears in a polynomial
Even Multiplicity The zero TOUCHES the x-axis, but does not cross it.
Odd Multiplicity The zero CROSSES the x-axis at this point.
End Behavior of an Even Degree Polynomial with a Positive Leading Coefficient The graph rises to the left and rises to the right.
End Behavior of an Even Degree Polynomial with a Negative Leading Coefficient The graph falls to the left and falls to the right.
End Behavior of an Odd Degree Polynomial with a Positive Leading Coefficient The graph falls to the left and rises to the right.
End Behavior of an Odd Degree Polynomial with a Negative Leading Coefficient The graph rises to the left and falls to the right.
Rational Zero Test A handy way to obtain a list of possible rational zeros of a function by listing all of the factors of the constant term and dividing by all of the factors of the leading coefficient.
Extrema All of the maximum and minimum values of a function
Relative Maximum On a small interval, a relative maximum occurs at a point in the interval where the graph is increasing prior to that point and decreasing after that point.
Relative Minimum On a small interval, a relative maximum occurs at a point in the interval where the graph is decreasing prior to that point and increasing after that point.
Absolute Maximum The highest point that a graph will reach. Please note only functions of even degree will have an absolute maximum.
Absolute Minimum The lowest point that a graph will reach. Please note only functions of even degree will have an absolute minimum.
Strictly Increasing A function is increasing if the y-values increase as the x-values increase.
Strictly Decreasing A function is decreasing if the y-values decrease as the x-values increase.
Created by: Kskeener