A sketch the graph of 1 3 2 y f x b sketch the graph

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a) Sketch the graph of ( ) 1 3 2 y f x = + . b) Sketch the graph of ( ) 1 y f x = . a) 1 mark for vertical compression (½ mark for left branch, ½ mark for right branch) 1 mark for horizontal shift (½ mark for left branch, ½ mark for right branch) 2 marks 1 1 x y ( ) 1, 0.5 ( ) 3, 1.5 ( ) 5, 1.5 1 x y ( ) 2, 1 ( ) 0, 3 ( ) 2, 3 1
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Pre-Calculus Mathematics: Marking Guide (January 2009) 29 Question 10 a) B6 b) B4 b) Note(s): any y -intercept between 1 and 0 is acceptable deduct a maximum of ½ mark for one or more endpoints or arrowheads incorrectly shown deduct ½ mark if graph crosses or curls away from the asymptote ½ mark for correctly placed asymptote ½ mark for left branch (arrowhead and endpoint) 1 mark for right branch (½ mark for correct graph on ( ] 1, 0 , ½ mark for correct graph on [ ] 0, 2 ) 2 marks 1 x y 1 ( ) 2, 1 1 2, 3
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30 Pre-Calculus Mathematics: Marking Guide (January 2009) Exemplars a) Mark: 1 out of 2 Note(s): gave 1 mark for horizontal shift b) Mark: 1½ out of 2 Note(s): gave ½ mark for correctly placed asymptote gave ½ mark for left branch gave ½ mark for correct graph on [ ] 0, 2
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Pre-Calculus Mathematics: Marking Guide (January 2009) 31 A2 11. If sec 0 and cot 0, then θ θ θ > < terminates in quadrant: a) I b) II c) III d IV C1 12. An expression equivalent to sin cos tan θ θ θ is: b 2 sin θ A3 13. If 3 sin 2 θ = − and θ terminates in quadrant IV, the exact value of cot θ is: c 1 3 Part 2: Multiple-Choice Questions
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32 Pre-Calculus Mathematics: Marking Guide (January 2009) A1 14. A central angle of 45 ° intercepts an arc 8 cm long. The radius of this circle is: a 32 cm π b) 2 cm π c) 8 cm 45 d) 45 cm 8 D3 15. If ( ) 2 log f x x = , then the inverse of this function is: b ( ) 1 2 x f x = 2 1 log f x x = A6 16. All the x -intercepts of the graph ( ) sin f x x = can be described by: a) k k π + π, ∈Ι 2 b) , k k π ∈Ι 2 c k k π, ∈Ι d) 0, , 2 π π
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Pre-Calculus Mathematics: Marking Guide (January 2009) 33 B3 17. If ( ) f x is an odd function, then: 1 f x f x = d ( ) ( ) f x f x = − B1 18. If ( ) 2 f x x = and the graph is shifted 2 units to the right, an equation for the resulting graph is: d ( ) 2 2 y x = D2 19. Solve the equation 3 9 81 x = i . b 3 2 x =
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34 Pre-Calculus Mathematics: Marking Guide (January 2009) D4
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  • Spring '12
  • A.Young
  • Trigonometry, Logarithm, New Testament chapters, pre-calculus mathematics

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