Rational functions are of the form y = f(x), where f(x) is a rational expression .
Some of the examples of rational functions are:
The graphs of the rational functions can be difficult to draw. To sketch a graph of a rational function, you can start by finding the asymptotes and intercepts.
Steps involved in graphing rational functions:
Graph the rational function
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
2 x + 1 = 0
x = -1/2
The vertical asymptote of the rational function is x = -0.5.
This function has the x -intercept at (-1/4, 0) and y -intercept at (0, 1). Find more points on the function and graph the function.
Sometimes the given rational function has to be simplified, before graphing it. In that case, if there are any excluded values (where the function is not defined) other than at asymptotes, then there is additional step involved in graphing the function.
To represent the undefined function, make sure that the function is not continuous smooth curve at the excluded value. This excluded value is usually referred to as hole in the rational function.
For example, the rational function has a hole at x = 0.
Please note that the graphs of the rational functions satisfy the vertical line test .