Lesson D11

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

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson D11, Graphs of y = 1/f(x) and y = |f(x)|: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

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

    • Where f(x) has a maximum
    • At the stationary points of f(x)
    • At the y-intercept of f(x)
    • At the zeros of f(x)

  2. On the graph of y = |f(x)|, what happens to the part of y = f(x) below the x-axis?

    • It is removed
    • It is reflected in the y-axis
    • It is reflected in the x-axis
    • It is translated up by 1

  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. For f(x) = x^2 + 1, what does the graph of y = |f(x)| look like?

    • A reflection of y = x^2 + 1 in the x-axis
    • A V shape with vertex at (0, 1)
    • Identical to y = x^2 + 1
    • The part above x = 0 only

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

    • 4.5
    • -2.25
    • 1.5
    • 2.25

  10. For f(x) = 2x + 4, which statement about y = 1/f(x) is correct?

    • x = 2 is a vertical asymptote and y = 0 is a horizontal asymptote
    • x = -2 is a vertical asymptote and y = 2 is a horizontal asymptote
    • x = -2 is a vertical asymptote and there is no horizontal asymptote
    • x = -2 is a vertical asymptote and y = 0 is a horizontal asymptote

  11. Near a zero a of f where f'(a) = 3, how does 1/f(x) behave?

    • It tends to 0 at x = a, since the reciprocal of a zero is very small
    • It tends to -infinity from the left and +infinity from the right
    • It stays finite at x = a, since the reciprocal of a zero is still defined
    • It tends to +infinity from both sides of x = a, since 1/f is always positive

  12. For f(x) = x^3 - x, what are the asymptotes of y = 1/f(x)?

    • Vertical asymptotes at x = -1 and 1 only, and y = 0
    • Vertical asymptotes at x = -1, 0 and 1, with no horizontal asymptote
    • Vertical asymptotes at x = -1, 0 and 1, and y = 0
    • A vertical asymptote at x = 0 and y = 1

  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. Which statement about y = |x^2 - 1| is correct?

    • It has minimum value 0 at x = -1 and x = 1
    • It has maximum value 0 at x = -1 and x = 1
    • It has minimum value -1 at x = 0
    • It never touches the x-axis

  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

All AQA Further Maths quizzes