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2.6 Rational Functions

2.6 Rational Functions. What is the graph of the parent rational function?. 2. How do you find the x intercept of a rational function ? Let y = 0 and solve. What mathematical “tools” will you need to accomplish this? The tools you will use depend on what the polynomial of the numerator is.

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2.6 Rational Functions

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  1. 2.6 Rational Functions What is the graph of the parent rational function?

  2. 2. How do you find the x intercept of a rational function? Let y = 0 and solve. What mathematical “tools” will you need to accomplish this? The tools you will use depend on what the polynomial of the numerator is. You may use factor and/or QF or simple solving. If the polynomial is of degree greater than 2 you may have to use the Remainder Thm and the Rational Root Thm ( P/Q) which involves using long/synthetic division and possibly evaluating.

  3. How do you find the y intercept of a rational function? Let x = 0 and evaluate. What mathematical “tools” will you need to accomplish this? No tools other than evaluating need.

  4. 4. How do you find the domain for a rational function? Use will employ the same tools as we did for finding the x intercept BUT this time we focus on the DENOMINATOR because we are setting the denominator equal to zero so we know which values for x must be limited from the domain because they would result in a division by zero error.

  5. How do you find the vertical asymptote? Simply by finding what values make the denominator equal to zero. This may be a simple as setting the denominator to 0 and solving but it may also require us to factor, use quadratic formula or the Rational Root Thm to solve Howdo you find the horizontal asymptote? Note: While we CANNOT intercept a VERTICAL asymptote we CAN intercept (touch/cross) a HORIZONTAL ONE We have three possible situations: IF the degree of the numerator < than degree of denominator the horizontal asymptote is : y = 0 IF the degree of the numerator = the degree of the denominator the horizontal asymptote is : the quotient of the leading coefficients. IF the degree of the numerator > than degree of the denominator there is no horizontal asymptote BUT…if the degree of the numerator is EXACTLY one more than the degree of the denominator then we have a slant asymptote which is determined through polynomial division. We MAY also have a HOLE.

  6. Reword the study tips they provided in this section below.

  7. Reword the “Guidelines for Analyzing Graphs of Rational Functions” on p.187

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