Chapter 13 Periodic Functions and Trigonometry

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• Lesson 8-3 Analyzing Graphs of Rational Functions

  Find the vertical asymptotes and holes for the graph of each rational function.

  1. y = 2 x − 3 y equals . fraction 2 , over x minus 3 end fraction
  2. y = x + 2 ( 2 x + 1 ) ( x − 4 ) y equals . fraction x plus 2 , over open , 2 x plus 1 , close . open , x minus 4 , close end fraction

• Lesson 8-4 Simplifying Complex Fractions

  Simplify each complex fraction.

  3. 2 a 1 b fraction fraction 2 , over eh end fraction , over fraction 1 , over b end fraction end fraction
  4. 5 + 1 2 2 − 1 5 fraction 5 plus , 1 half , over 2 minus , 1 fifth end fraction
  5. 3 c + d 2 fraction fraction 3 , over c plus d end fraction , over 2 end fraction
  6. 1 4 4 c fraction 1 fourth , over fraction 4 , over c end fraction end fraction
  7. 2 3 6 c + 4 fraction 2 thirds , over fraction 6 , over c plus 4 end fraction end fraction
  8. 4 x 2 8 fraction fraction 4 , over x end fraction , over 2 eighths end fraction
  9. 3 − 1 2 7 6 fraction 3 minus , 1 half , over 7 sixths end fraction
  10. 9 m − n 3 2 m − 2 n fraction fraction 9 , over m minus n end fraction , over fraction 3 , over 2 m minus 2 n end fraction end fraction

• Lesson 9-1 Writing Formulas for Sequences

  Find the next two terms in each sequence. Write a formula for the nth term. Identify each formula as explicit or recursive.

  11. 16 , 13 , 10 , 7 , … 16 comma 13 comma 10 comma 7 comma dot dot dot
  12. − 1 , − 8 , − 27 , − 64 , − 125 , … negative 1 comma negative 8 comma negative 27 comma negative 64 comma negative 125 comma dot dot dot

• Lesson 10-6 Translating Conic Sections

  Write an equation for each conic section. Then sketch the graph.

  13. circle with center at ( 1 , − 4 ) open 1 comma negative 4 close  and radius 4
  14. ellipse with center at (2, 5), vertices at (5, 5) and ( − 1 , 5 ) , open negative 1 comma 5 close comma  and co-vertices at (2, 3) and (2, 7)
  15. parabola with vertex at ( 0 , − 3 ) open 0 comma negative 3 close  and focus at (0, 5)
  16. hyperbola with center at (6, 1), one focus at (6, 6), and one vertex at ( 6 , − 2 ) open 6 comma negative 2 close

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