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Grade 11 · Functions
Hyperbola & Exponential Graphs (Grade 11)
MEMORANDUM
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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
    Write down the asymptotes of y = 4x − 1 + 2.
    (2)
    x = 1y = 2-6-4-22468-6-4-22468xy(−1 ; 0)(0 ; −2)
    x = 1 and y = 2✓✓ (2)
  2. 2
    Determine the y-intercept of y = 4x − 1 + 2.
    (2)
    4−1 + 2 = −2✓✓ (2)
  3. 3
    Determine the x-intercept of y = 4x − 1 + 2.
    (2)
    4 = −2(x − 1) → x = −1✓✓ (2)
  4. 4
    Write down the domain and range of y = 4x − 1 + 2.
    (2)
    Domain x ∈ ℝ, x ≠ 1; range y ∈ ℝ, y ≠ 2✓✓ (2)
  5. 5
    Write down the equation of the asymptote of y = 2x − 1.
    (2)
    y = −1-4-3-2-11234-4-2246810xyy = 2x − 1(0 ; 0)
    y = −1✓✓ (2)
  6. 6
    Determine the y-intercept of y = 2x − 1.
    (2)
    2⁰ − 1 = 0✓✓ (2)
  7. 7
    Write down the range of y = 2x − 1.
    (2)
    y > −1✓✓ (2)
  8. 8
    Describe the transformation from y = 2x to y = 2x − 1.
    (2)
    A translation of 1 unit downwards✓✓ (2)
TOTAL: 16 marks
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