Rational Functions: Graphs, Applications, and Models Chapter 3.5 Rational Functions: Graphs, Applications, and Models

The Reciprocal Function The simplest rational function with a variable denominator is called the reciprocal function, defined by

The Reciprocal Function The domain of this function is the set of all real numbers except 0. The number 0 cannot be used as a value of x, but it is helpful to find values of f(x) for some values of x close to 0.

The Reciprocal Function The domain of this function is the set of all real numbers except 0. The number 0 cannot be used as a value of x, but it is helpful to find values of f(x) for some values of x close to 0.

The Reciprocal Function We use the table feature of a graphing calculator to do this. The tables in Figure 37 suggest that |f(x)| gets larger and larger as x gets closer and closer to 0, which is written in symbols as

The Reciprocal Function

The Reciprocal Function

The Reciprocal Function

The Reciprocal Function

The Reciprocal Function

y x

y x

y x

Steps for Graphing Rational Functions A comprehensive graph of a rational function exhibits these features: all x- and y-intercepts; all asymptotes: vertical, horizontal or oblique. the point at which the graph intersects its non-vertical asymptote (if there is any such point. enough of the graph to exhibit the correct end behavior.

x

x

x

x

x