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Reading answers off a graph

Mathematics · Algebra · ages 13-14

Name ______________________ Date ____________

At x = -3, a curve's height is halfway between the y-axis ticks -2 and -1. What is the estimated y-value?
Answer: ______________
A drawn curve meets the horizontal line y = 5 at (-2, 5) and (4, 5), and nowhere else in the drawing. How many shown inputs give output 5?
- One input
- Three inputs
- Two inputs
- Five inputs
Two graphs meet at (-2, 8). What is their shared output at that meeting?
Answer: ______________
A distance-from-home graph has time in hours on the horizontal axis and distance in kilometres on the vertical axis. It contains the point (3, 6). What does this point mean?
- The hiker has walked for 6 hours by that point
- The hiker is 6 km from home after 3 hours
- The hiker is moving at exactly 6 km per hour
A graph reading gives y = 3 at x = 1 and y = 12 at x = 4. How much did y increase from x = 1 to x = 4? Type the number.
Answer: ______________
A drink's temperature-time graph falls quickly, then continues falling along a less steep curve. The axis scales stay the same. What does the later part show?
- The temperature is rising more slowly than before
- The temperature has become exactly constant there
- The time is passing more slowly than before
- The temperature is falling more slowly than before
A graph is drawn only for -1 ≤ x ≤ 1 and has no x-axis meeting there. This proves its rule has no zero-output inputs anywhere.
Circle one: True False
A curve touches the x-axis at (-1, 0), turns upwards, and has no other x-axis meeting. What solution does this give when its rule is set equal to zero?
- No solution, because touching does not count
- One solution, given by the input x = -1
- Two solutions, because the curve turns upwards
- One solution, given by the output y = 0
An object travels on a straight route towards or away from home. Maya reads its distance-from-home graph: 'The line goes down between minute 5 and minute 10, so the object is speeding up.' What should she check?
- Whether distance is increasing; any downward line means the object has stopped
- The slope's steepness; falling distance only means getting closer
- Whether time is increasing; any downward line means the object is moving faster
The graph of y = x² is drawn only for 0 ≤ x ≤ 5. Ben wants to read y at x = -2 directly from this drawing. Can he?
- Yes, because -2 is an input in the drawn interval
- Yes, because every curve repeats outside its drawn interval
- No, because -2 is outside the drawn interval

Answer key

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

Reading answers off a graph W1-mt_Yw27nweoTj-s1

-1.5 · Halfway from -2 to -1 is -1.5.
Two inputs · The two meeting points give two different inputs, -2 and 4, with output 5.
8 · The shared output is the y-coordinate, 8. The input at the meeting is -2.
The hiker is 6 km from home after 3 hours · The first coordinate gives time, 3 hours. The second gives distance from home, 6 km. One point alone does not give speed.
9 · Subtract the starting output from the final output: 12 - 3 = 9.
The temperature is falling more slowly than before · The curve still falls, so cooling continues. Its smaller slope magnitude on the same scales shows slower cooling.
False · The drawing shows no zero-output inputs in its displayed interval. It gives no graphical reading outside that interval.
One solution, given by the input x = -1 · A touching point also has output zero. Its input -1 is the single solution.
The slope's steepness; falling distance only means getting closer · Falling distance means the object is getting closer to home. Increasing speed requires increasing slope magnitude, using the axis units.
No, because -2 is outside the drawn interval · The drawing contains no curve at input -2. Ben could calculate from the rule, but he cannot read that value directly from this drawing.