Reading solutions from a graph · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading answers off a graph

Mathematics · Algebra · ages 13-14
Name ______________________   Date ____________

  1. The graph of y = 3x - 2 is drawn on a grid. What is the value of y when x = 5?

    Answer: ______________

  2. The graph of a function crosses the x-axis at (-3, 0) and (1, 0). What are the solutions of f(x) = 0?

    • x = -3 and x = 1
    • x = 3 and x = -1
    • x = 0 only
    • There are no solutions

  3. Two lines are drawn on the same axes: y = x + 1 and y = 7. At what x-value do the two lines meet?

    Answer: ______________

  4. A distance-time graph shows a hiker's distance from home. At 3 hours, the graph shows the hiker is at 6 km from home. What does this tell you?

    • The hiker is 6 km from home after 3 hours
    • The hiker walked for 6 hours
    • The hiker's speed is 6 km per hour

  5. A curve is plotted. At x = 1, the curve is level with y = 3. At x = 4, the curve is level with y = 12. Using the graph, how much did y increase from x = 1 to x = 4? Type the number.

    Answer: ______________

  6. A graph shows the temperature of a drink cooling over time. The line drops quickly at first, then levels off flat near room temperature. What does the flat part of the graph mean?

    • The drink is warming back up
    • The drink stopped changing temperature
    • Time has stopped
    • The graph is broken

  7. If the graph of a function never touches the x-axis, then the equation f(x) = 0 has no real solutions.

    Circle one:   True   False

  8. The graph of y = x² - 9 crosses the x-axis at two points. What are the solutions of x² - 9 = 0?

    • x = -3 and x = 3
    • x = -9 and x = 9
    • x = 0
    • No real solutions

  9. Maya looks at a distance-time graph. She says: 'The line goes down between minute 5 and minute 10, so the object is speeding up.' What is wrong with her reasoning?

    • A downward line means distance is decreasing, not that speed is increasing
    • A downward line means the object has stopped
    • Nothing is wrong; downward always means faster

  10. A graph of y = x squared is drawn only for x-values between 0 and 5. Ben wants to use this graph to estimate y when x = -2. Can he read this off the graph?

    • No, because the graph was never drawn for x = -2
    • Yes, just read off x = -2 as normal
    • Yes, because curves always repeat outside the drawn part
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Answer key

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

Reading answers off a graph W1-mt_Yw27nweoTj-s1

  1. 13 · Going up from x = 5 on the graph lands on y = 13.
  2. x = -3 and x = 1 · The solutions are the x-coordinates of the crossings: -3 and 1.
  3. 6 · The lines meet at x = 6, where both give y = 7.
  4. The hiker is 6 km from home after 3 hours · The point (3, 6) means 3 hours have passed and the hiker is 6 km from home. It doesn't directly give speed or total walking time.
  5. 9 · Read both y-values off the graph, then subtract: 12 - 3 = 9.
  6. The drink stopped changing temperature · A flat part on a temperature graph means the temperature is no longer changing as time passes.
  7. True · Solutions of f(x) = 0 are exactly where the graph meets the x-axis, so no crossing means no solutions.
  8. x = -3 and x = 3 · The graph crosses at (-3, 0) and (3, 0), so the solutions are -3 and 3.
  9. A downward line means distance is decreasing, not that speed is increasing · A downward line means the object is getting closer to the start. Speed comes from how steep the line is, not which way it slopes.
  10. No, because the graph was never drawn for x = -2 · You can only read approximate values from the part of the graph that's actually plotted. Outside that range, there's nothing to read.
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