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Grade 10 · Functions and Graphs
The Hyperbola & Exponential Graph (Grade 10)
MEMORANDUM
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  / 14

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    What are the asymptotes of y = 6/x?
    (2)
    x = 0 and y = 0✓✓ (2)
  2. 2
    What are the asymptotes of y = 4/x − 3?
    (2)
    x = 0 and y = −3✓✓ (2)
  3. 3
    In which quadrants does y = 6/x lie?
    (1)
    1 and 3 (since a > 0)✓ (1)
  4. 4
    In which quadrants does y = −5/x lie?
    (1)
    2 and 4 (since a < 0)✓ (1)
  5. 5
    Why does a hyperbola have no y-intercept?
    (2)
    x cannot be 0 — you cannot divide by zero.✓✓ (2)
  6. 6
    Find y when x = 3 for y = 6/x.
    (1)
    y = 2✓ (1)
  7. 7
    What is the y-intercept of y = 2x?
    (1)
    (0 ; 1)✓ (1)
  8. 8
    What is the asymptote of y = 2x + 5?
    (1)
    y = 5✓ (1)
  9. 9
    Find the y-intercept of y = 3·2x − 4.
    (2)
    y = 3(1) − 4 = −1, so the intercept is (0 ; −1)✓✓ (2)
  10. 10
    Does y = (½)x increase or decrease?
    (1)
    Decreases — the base is between 0 and 1.✓ (1)
TOTAL: 14 marks
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