D11 Graphs of y = 1/f(x) and y = |f(x)| Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Where does the graph of y = 1/f(x) have vertical asymptotes?

   • y-intercepts
   • Stationary points
   • Infinite limits
   • Zeros of f(x)

2. How is the portion of y = f(x) below the x-axis transformed for y = |f(x)|?

   • Translated upwards
   • Reflected in y-axis
   • Reflected in x-axis
   • Deleted entirely

3. If f(3) = 2, what is the value of 1/f(x) at x = 3?

   • 2
   • 3
   • 1/2
   • -2

4. For f(x) = x - 2, what is the value of y = 1/f(x) at x = 0?

   • -2
   • 0
   • -1/2
   • 1/2

5. For f(x) = x^2 - 4, what is |f(0)|?

   • 2
   • 0
   • 4
   • -4

6. For f(x) = x^2 - 1, which vertical asymptotes does y = 1/f(x) have?

   • x = 1 and x = -1
   • x = 1 only
   • x = 0 only
   • x = 2 and x = -2

7. For f(x) = x^2 + 1, which feature does y = 1/f(x) have?

   • A maximum point at (0, -1)
   • A vertical asymptote at x = 0
   • A minimum point at (0, 1)
   • A maximum point at (0, 1)

8. What is the relationship between the graphs y = |x^2 + 1| and y = x^2 + 1?

   • Reflected in x-axis
   • Translated upwards
   • Identical graphs
   • Reflected in y-axis

9. For f(x) = x(x - 3), what is |f(1.5)|?

   • 4.5
   • -2.25
   • 1.5
   • 2.25

10. What is the vertical asymptote of the graph y = 1/(2x + 4)?

    • x = 2
    • x = -4
    • x = 0
    • x = -2

11. As x approaches a root of f(x) from the left with f'(a) > 0, what value does 1/f(x) approach?

    • Zero
    • Minus infinity
    • Three
    • Plus infinity

12. How many vertical asymptotes does the graph of y = 1/(x^3 - x) have?

    • One
    • Two
    • Three
    • None

13. How many solutions does |f(x)| = 2 have when f(x) = x^2 - 4?

    • 2
    • 3
    • 4
    • 0

14. What is the maximum of |f(x)| on [0, 2] for f(x) = x^2 - 2x - 3?

    • 4
    • 2
    • 0
    • 3

15. For f(x) = x^2 + 2x + 5, what is the maximum value of y = 1/f(x) and where does it occur?

    • 1/4 at x = -1
    • 1/5 at x = -2
    • 4 at x = -1
    • -1/4 at x = -1

16. What is the minimum value of the function y = |x^2 - 1|?

    • 0
    • 1
    • -1
    • 2

17. How many turning points does y = |x^2 - 1| have?

    • 4
    • 1
    • 3
    • 2

18. For f(x) = x - 3, what is y = 1/f(x) at x = 5?

    • 2
    • 1/8
    • -1/2
    • 1/2

19. For f(x) = x^2 - 9, how many vertical asymptotes does y = 1/f(x) have?

    • 0
    • 4
    • 1
    • 2

20. For f(x) = 2 - x, what is the value of |f(5)|?

    • 2
    • -3
    • 3
    • 7

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