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Warm UP!

Warm UP!. Factor the following:. Unit 7: Rational Functions. LG 7-1: Characteristics & Graphs LG 7-2: Inverses LG 7-3: Solving Equations & Inequalities TEST: 4/03. LG 7-1 Graphs & Characteristics of Rational Functions.

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Warm UP!

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  1. Warm UP! Factor the following:

  2. Unit 7: Rational Functions LG 7-1: Characteristics & Graphs LG 7-2: Inverses LG 7-3: Solving Equations & Inequalities TEST: 4/03

  3. LG 7-1 Graphs & Characteristics of Rational Functions By the end of today, you will know how to find the following characteristics algebraically: Domain and Range x-intercepts and y-intercepts Horizontal and vertical asymptotes Holes **Important Note: Rational Functions should always be FACTORED before you do ANYTHING! If you skip this step, then you will probably do more work then you needed to!

  4. For example… You WILL be able to take the following problem and make a list of these characteristics: Holes: Domain: Range: x-intercepts: y-intercepts: Horizontal asymptotes: Vertical asymptotes:

  5. Notes If you can cancel a factor in both the numerator and the denominator, then a rational function has a hole. To find the x-coordinate, set the canceled factor equal to zero and solve. Then plug that value into “the leftovers” to find the y-coordinate. Example: Hole HOLE: (3, 1/7)

  6. Practice Determine if the function has a hole. If so, find the coordinates.

  7. Domain What is the domain of this function? • How to find the DOMAIN: Set your denominator equal to zero and solve. This number is NOT included as a value for x. You will also exclude the x-value of the hole if applicable.

  8. Practice Find the Domain.

  9. Range • Find the degreeof the numerator and denominator. • If the degrees are equal take the coefficients of the leading terms. This number is excluded from the range. • If the degree of the numerator is smaller than the denominator then 0 is excluded. • If the degree of the numerator is bigger than the denominator, then the range is all real numbers.

  10. Practice Find the Range:

  11. X-intercepts To find the x-intof Rational Functions, set the numerator equal to zero and solve for x.

  12. Practice Find all x-intercepts of each function.

  13. y-intercepts To find the y-intof Rational Functions, substitute 0 for x.

  14. Practice Find all y-intercepts of each function.

  15. Vertical Asymptotes A rational function has a vertical asymptote at each value of x that makes only the denominator equal zero. It’s value is the numbers you used to state the domain restrictions! written as x = # Domain: Vertical Asymptotes:

  16. Practice Find the Vertical Asymptotes:

  17. Horizontal Asymptote A rational function has a horizontal asymptote at each value of y that is not defined. It’s value is the numbers you used to state the range restrictions! written as y = # Range: Horizontal Asymptote:

  18. Practice Find the Horizontal Asymptotes:

  19. Class Work

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