Domain

• All the possible values of the independent variable, x, for which y is defined

Undefined values in rational functions

• Rational functions always take the form, y = p(x) / g(x), where p(x) & g(x) are both polynomials

• Undefined values in the domain are found by setting factors in the denominator = 0. Undefined values show up as asymptotes or discontinuities on a graph

• Vertical asymptotes: a line that continually approaches a given curve but does not meet it at any finite distance.

• Discontinuity: a break in a line that shows up as an open circle in a graph

• Undefined values in the domain are also found by determining the value under a square root is < 0

EXAMPLES

• y = (x – 3) / ((x – 3) (x – 4))

x = 3 & x = 4 are undefined values and they are not in the domain

x = 4 is a vertical asymptote ((x – 4) is a factor in only the denominator)

x = 3 is a discontinuity in the graph ((x – 3) is a factor in both the numerator & denominator)-it appears as an open circle in the graph