Find Rational Functions (1)
This is an analytical tutorial on rational functions to further understand the properties of the rational functions and their graphs. The examples have detailed solutions in this page, the matched exercises have answers here.
Example 1 : Find the equation of the rational function f of the form
whose graph has a y intercept at (0 , -1) and has a vertical asymptote at x = 2. Solution to Example 1:
Matched Exercise 1: Find the equation of the rational function f of the form
whose graph has a y intercept at (0 , -1/4) and has a vertical asymptote at x = -1. Answer to Matched Exercise 1
Example 2 : Find the equation of the rational function f of the form
whose graph has ax x intercept at (2 , 0), a vertical asymptote at x = -1 and a horizontal asymptote at y = 1/2. Solution to Example 2:
Check answer graphically: The graph of the rational function obtained is shown below. Check the x intercept, the vertical and the horizontal asymptotes.
Matched Exercise 2: Find the equation of the rational function f of the form
whose graph has ax x intercept at (1 , 0), a vertical asymptote at x = -1 and a horizontal asymptote at y = 2. Answer to Matched Exercise 2 More References and Links to Rational FunctionsGraphs of rational functionstutorial on graphs of rational functions self test on graphs of rational functions. Solver to Analyze and Graph a Rational Function |