Rational and Integer Value Functions

Rational Functions

• A rational function can be represented as the division of two polynomial functions P(x) and Q(x).
• The general form of a rational function is $f(x) = \frac{P(x)}{Q(x)}$, where Q(x) cannot be equal to zero.

Integer Value Function

• The integer value function, denoted by $f(x) = [x]$, maps a real number x to the greatest integer less than or equal to x.
• The function can be expressed as $f : R \rightarrow Z$ where $x \rightarrow [x]$.

Function Values

• The integer value of 4.1 is 4.
• The integer value of -4/3 is -2.
• The integer value of $\pi$ is 3.
• The integer value of -$\pi$ is -4.

Graphs of Functions

• A function can be defined differently for different intervals of x.
• Examples of function values are:
  • f(2) = 0
  • f(3) = 10
  • f(4) = 17
  • f(7) = 4