Recognising Cubic, Reciprocal and Exponential Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Recognising Cubic, Reciprocal and Exponential Graphs

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. On the curve y = 2 to the power of x, when x is 4, what is y?

    • 8
    • 32
    • 4
    • 16

  2. The cubic is an odd shape, so the point (4, 64) on y = x cubed has a partner at:

    • (-4, 64)
    • (4, -64)
    • (-4, -64)
    • (64, 4)

  3. Which of these points sits on the curve y = x cubed?

    • (5, 125)
    • (4, 16)
    • (6, 18)
    • (3, 9)

  4. The reciprocal y = 1/x crosses the x-axis.

    Circle one:   True   False

  5. A point on the curve y = x cubed has y-coordinate 216. What is its x-coordinate?

    Answer: ______________

  6. A petri dish of bacteria doubles in size every hour. Which shape best describes the graph of the number of bacteria against time?

    • the cubic
    • the reciprocal
    • the exponential
    • a straight line

  7. The curve y = 1/(x + 3) has a horizontal asymptote at y = 0.

    Circle one:   True   False

  8. On the curve y = 1/x, what is the difference between the y-values at x = 1/10 and x = 1/5?

    Answer: ______________

  9. Dev sketches y = 2 to the power of x as a straight line through (0, 1), saying the output grows by 2 each time x increases by 1. Where is the slip?

    • the output multiplies by 2 each step, which bends the curve
    • the output adds 2 each step
    • the curve should pass through the origin
    • 2 to the power of x is always 2

  10. For the shifted curve y = (1/x) + 2, what is y when x is 5?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Recognising Cubic, Reciprocal and Exponential Graphs W1-mt_2IJJ51rmq9-s1

  1. 16 · 2 to the power 4 is 2 times 2 times 2 times 2, which is 16.
  2. (-4, -64) · A half turn around the origin flips both coordinates, so (4, 64) pairs with (-4, -64). Indeed (-4) cubed is -64.
  3. (5, 125) · Cube each x-value: 5 cubed is 125, which matches. 4 cubed is 64, not 16; 6 cubed is 216, not 18; 3 cubed is 27, not 9.
  4. False · The curve would cross the x-axis where y = 0, but 1/x never equals 0. It only gets closer and closer.
  5. 6 · The rule says y = x cubed, so x cubed = 216, and 6 cubed is 216, so x = 6.
  6. the exponential · Doubling each hour means multiplying by the same factor, so the growth speeds up. That is the exponential shape, not a straight line.
  7. True · The +3 only slides the curve sideways, so the tails still slide toward the x-axis, and y gets closer and closer to 0 as x grows.
  8. 5 · At x = 1/10, y is 10. At x = 1/5, y is 5. The difference is 10 - 5 = 5, the climb as x nears zero.
  9. the output multiplies by 2 each step, which bends the curve · Going from x to x + 1 multiplies the output by 2, it does not add 2. Multiplicative growth is what bends the exponential curve, while adding 2 would give a straight line.
  10. 2.2 · 1/5 is 0.2, and adding 2 gives 2.2. The +2 shifts the whole curve up.
Worksheet · LightMySky