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4.1  Vocabulary

Asymptote

An asymptote of a curve is a way of describing its behavior far away from the origin or very close to a specific value by comparing it to another curve.   For many rational functions, the asymptotes are vertical or horizontal lines.  As the input tends toward positive or negative infinity, the outputs get arbitrarily close to the horizontal asymptote.  As the inputs get arbitrarily close to the vertical asymptote, the outputs tend toward positive or negative infinity.  The graph of a function and its vertical asymptote(s) never meet.  A graph may cross a horizontal asymptote.

Decreasing function

A function f  is decreasing on an open interval if for all a and b in that interval  implies .  Informally, if the graph of a function falls from left to right over an interval, it is said to be decreasing on that interval.

Domain of a function

Set of inputs of a function.  With traditional notation, the domain is the set of x values that result in real number outputs. 

End Behavior

The behavior of function outputs as the input approaches positive or negative infinity.  Common end behaviors are tending toward positive or negative infinity (polynomials) or tending toward a horizontal asymptote.

Increasing Function

A function f  is increasing on an open interval if for all a and b in that interval  implies .  Informally, if the graph of a function rises from left to right over an interval, it is said to be increasing on that interval.

Polynomial

A polynomial function P is given by  

Where the coefficients  are real numbers and the exponents are whole numbers.

Range

The output values of a function.  With traditional notation, the range is the set of y values of a function.  One way of determining the range is to examine the graph of the function.  In particular note the values along the y-axis that are outputs on the graph.

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