Graphs 7
4 marks · NormalA student draws the graph of for .
| x | y |
|---|---|
| -2 | -1 |
| -1 | 3 |
| 0 | 1 |
| 1 | -1 |
| 2 | 3 |
| 3 | 19 |
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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Also accept: Answers based on interpreting table values for given equations or using graphical logic.
Common mistakes: Mixing up x and y, reading wrong row or not showing working.
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Marking points
B1 · 1 mark · States values of y when x = -1, 0, 1 correctly from the table.
B2 · 1 mark · Correctly estimates the value(s) of x for which y = 0 (using table logic or interpolation).
B3 · 1 mark · Correctly estimates the value(s) of x for which y = 4 (between -2 and -1, or 1 and 2 as appropriate).
B4 · 1 mark · Justifies estimates by referring to the changes in y as x increases (interpolation/logic).
Worked solution
From the table:
y=0 between x=1 and x=0 (since y=1 at x=0, y=-1 at x=1). By linear interpolation, x ≈ 0.5.
y=4 between x=2 (y=3) and x=3 (y=19); since 3 to 19 is a big jump, estimate x ≈ 2.1 for y=4 by interpolation.
All required values are extracted and justified using the trend in y-values.