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Graphs of Rational Functions
In this example, a rational function with one vertical asymptote is graphed.
Review of graps of rational functions:
A rational function can be written as the ratio of two functions, f(x) and g(x). Rational functions are usually written in this form:
y = f(x)/g(x)
Since division by zero is undefined, then with all rational functions written in the form shown above, the function g(x) cannot equal zero. In fact, the graphs of rational functions have a characteristic shape around the values of x where g(x) cannot equal zero.
The graphs of rational functions have vertical asymptotes, based on the values of x where g(x) equals zero. A vertical boundary line defines the place where the graph of the rational function approaches but does not equal this value of x.
In this set of Math Tutorials we analyze the rational functions, identify the vertical asymptotes, and then graph the function. You should use a graphing calculator to graph the rational function and identify the asymptotes.
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The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
Our current inventory of Math Examples include:
- Math Tutorial: Examples Using Algebra Tiles
- Math Tutorial: Solving Equations in One Variable
- Math Tutorial: Solving Equations with Fractions
- Math Tutorial: Solving Equations with Percents
- Math Tutorial: Slope formula
- Math Tutorial: Midpoint formula
- Math Tutorial: Distance formula
- Math Tutorial: Graphing linear functions, given m and b
- Math Tutorial: Graphing absolute value functions
- Math Tutorial: Graphing linear inequalities
- Math Tutorial: Using the Point-Slope form
- Math Tutorial: Finding the equation of a line given two points
- Math Tutorial: Graphing parallel and perpendicular lines
- Math Tutorial: Solving quadratics graphically
- Math Tutorial: Solving quadratics by completing the square
- Math Tutorial: Factoring Quadratics
- Math Tutorial: Polynomial Expansion
- Math Tutorial: Solving quadratics using the quadratic formula
- Math Tutorial: Using FOIL
- Math Tutorial: Graphs of Exponential Functions
- Math Tutorial: Laws of Exponents
- Math Tutorial: Graphs of Logarithmic Functions
- Math Tutorial: Graphs of Rational Functions
- Math Tutorial: Combining Rational Expressions
- Math Tutorial: Graphs of Conic Sections
