A rational function is a function that can be written as the quotient of two polynomials.

Since rational functions are made up of polynomial functions, there are characteristics of the graphs that are similar to other functions, including possible x-intercepts or y-intercepts. However, some characteristics of rational functions are very different from other function families. Those characteristics also create graphs that are different from other graphs that you have studied.

Parent Function:

f(x) = 1 over x 1 x

Degree of Numerator: 0

Degree of Denominator: 1

f(x) = x + 2 over x squared + 5x + 6 x + 2 x2 + 5x + 6

Degree of Numerator: 1

Degree of Denominator: 2

f(x) = x squared + 7x + 12 over x squared + 5x + 6 x2 + 7x + 12 x2 + 5x + 6

Degree of Numerator: 2

Degree of Denominator: 2

In this lesson, you will investigate connections between the parameters in the rational function and the attributes of the graph that result.

Key attributes that you will examine include asymptotes, or lines that the graph will approach but never touch, and removable discontinuities, or holes that appear in the graph of a rational function where there are no numerical values of y that make sense for the function for the corresponding value of x.