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Turn to the Rational Functions part of your binder

Turn to the Rational Functions part of your binder. January 19, 2012. Rational Functions. A rational function is a function of the form Where p and q can be polynomial functions of x How would you find the domain of the following function

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Turn to the Rational Functions part of your binder

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  1. Turn to the Rational Functions part of your binder January 19, 2012

  2. Rational Functions • A rational function is a function of the form Where p and q can be polynomial functions of x • How would you find the domain of the following function • The rule of fractions is you cannot have a 0 in the denominator • A vertical asymptote is created where the denominator is equal to 0

  3. Vertical Asymptotes • A vertical asymptote is a vertical line where a function is undefined • The graph of the function on either side of the asymptote extends to either positive or negative infinity. • The line will approach the asymptote but will never intersect

  4. Domain & Asymptote • The domain refers to all of the possible x values the function can have • Asymptotes tell you all of the x values that a function cannot have • What is the domain? • Where is the asymptote?

  5. Find the domain and asymptote of the following functions Home work

  6. Rational Function Review • A rational function is a ratio or fraction of two polynomial functions , where q(x)≠0 • An asymptote is a line that a graph approaches but never intersects • Domain of a rational function is all real numbers(ℝ), where x ≠ 0 (asymptote)

  7. Vertical Asymptote • Is a vertical line that intersects the x axis of the form x = a • To find a vertical asymptote: • Take the denominator of the rational function and set it to equal to 0 • Solve for x • VA: x = a Example:

  8. Horizontal Asymptote • Is a horizontal line that intersects the y axis of the form y = b • Method 1: • Make f(x) = y • Multiply both sides of equation by denominator • Distribute y • Get x’s on one side y’s on other • Factor • Divide each side by parenthesis • Set denominator equal to 0, solve for y

  9. You try: • What is the horizontal asymptote of:

  10. Homework • Using the following function: • Find the domain • Vertical Asymptote • Horizontal Asymptote • Graph

  11. Roots of a rational function • A root- is a solution of the equation P(x) = 0 • Where the graph of a function intersects the x-axis • In a rational function roots are only found if there is an x variable in the numerator • Steps to find root: • Set Numerator equal to zero • Solve for x

  12. Y-intercept • Is where the graph of a function intersects the y-axis • The value of the y variable when x is 0 • Steps to find a y intercept: • Plug in zero for your x • Solve

  13. Lets Put it All Together • Using the following rational function • Find the root and y-intercept • Find the domain • Find the Vertical Asymptote • Find the Horizontal Asymptote • Graph

  14. Horizontal Asymptote • If the degree in the numerator is larger than that of the denominator there is no horizontal asymptote • When the degree in the numerator is less than that of the denominator the H.A is y=0

  15. H.A. continued… • When the degree of the numerator is equal to that of the denominator use the following method: • Method 2: • compare the coefficients in front of the terms with the highest power. • The horizontal asymptote is the coefficient of the highest power of the numerator divided by the coefficient of the highest power of the denominator

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