Rational functions
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Rational functions have two types of asymptotes: vertical asymptotes which are found by making the denominator equal to zero, and horizontal asymptotes which come in three types based on the degrees of the numerator and denominator. To graph a rational function, you first find the vertical and horizontal asymptotes, then locate the x-intercepts, y-intercept and use a calculator to generate a table of values to graph points and draw the line. The domain is all real numbers except values making the denominator equal to zero, and the range is all real numbers.
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Rational functions
- 2. Asymptotes2 Different kinds of asymptotes:1) Vertical Asymptote: x=______(something)**Never cross vertical asymptotes/Always make the denominator 0.2) Horizontal Asymptote: y=______(something)**Can be crossed/3 different types
- 3. 3 Types of Horizontal AsymptotesType 1: When the degree of the denominator is LARGER than the degree of the numerator. y=0Type 2: When the numerator degree and the denominator degree are the SAME.Type 3: When the numerator degree is LARGER than the denominator degree.
- 4. How To Make A Rational FunctionThe rational function (f) has the equation:You need to find the Vertical Asymptotes(VA) which is the opposite of the number in the denominator: 3You need to find the Horizontal Asymptotes(HA), which is always equal to 0 if the denominator is larger than the numerator: y=0
- 5. How To Make A Rational FunctionFor the x-intercept you set the numerator to zero and solve from there: x=(2, 0)For the y-intercept you use the tables on the calculator and answer what the y-intercept is next to the 0: y=(0, -.66)To find the tables on your calculator you type in your rational function in theY= tab and 2nd graph to get your tables, in which you find the matching pair of each number.Tables:
- 6. GraphGraph the numbersyou find on yourtable and connectthem to get your lines on yourgraph: Find Domain and Range:D:(-∞,3)U(3,∞)R:(-∞,0)U(0,∞)