2.5.1 Reciprocal and Rational Functions TBC

Reciprocal Function Definition

The reciprocal function is defined by f(x) = 1/x, x ≠ 0

Reciprocal Function: Domain

Its domain is the set of all real values except 0

Reciprocal Function: Range

Its range is the set of all real values except 0

Reciprocal Function: Self-Inverse

The reciprocal function has a self-inverse nature, meaning that taking the inverse doesn’t change the function

• f^-1(x) = f(x)

• (f o f)(x) = f(x)

Key Features of the Reciprocal Graph

Linear Rational Function Definition

Fact: The reciprocal function is a special case of a rational function

Linear Rational Functions: Domain

Linear Rational Functions: Range

Key Features of Linear Rational Graphs

Linear Rational Graphs Tip

• Drawing a horizontal line anywhere should only intersect this type of graph once at most

• The only horizontal line that should not intersect the graph is the horizontal asymptote