Domain and Range
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Domain and Range — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionRange from graphsConcept Practice
2 marks~3 minCriterion A
A delivery drone travels in a straight line between two checkpoints. Its horizontal distance xx (in km) from the launch pad satisfies −2≤x≤3-2 \leq x \leq 3. The drone's altitude (in metres) is modelled by f(x)=2x+1f(x) = 2x + 1.
a
State the range of ff for the given domain. [1]
b
The drone must maintain an altitude strictly above −1-1 m throughout the journey. Justify whether this safety condition is met. [1]
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Solutions

2QuestionDomain from graphsAssessment Practice
4 marks~6 minCriterion C
A city's water pressure monitoring system records pressure (in bar) as a piecewise linear function of time (in hours) over a 24-hour period. Due to scheduled maintenance, no data is recorded between t=−1t = -1 and t=1t = 1.

The graph shows two linear segments:
- Segment 1: from (−4, 2)(-4,\ 2) (closed circle) to (−1, 5)(-1,\ 5) (open circle)
- Segment 2: from (1, 3)(1,\ 3) (closed circle) to (4, 0)(4,\ 0) (closed circle)
a
Justify whether this graph represents a function. [1]
b
Deduce the domain of the function, expressing your answer in interval notation. [1]
c
The monitoring system requires at least 7 hours of combined recorded data to be considered reliable. Advise the network operator whether this session meets the reliability requirement, supporting your answer with calculations. [2]

Solutions

3QuestionRange from graphsAssessment Practice
6 marks~9 minCriterion D
A rocket is launched from ground level. Its predicted height hh (in metres) at time tt (in seconds) is modelled by

h(t)=−5t2+20t.h(t) = -5t^2 + 20t.

Experimental measurements were recorded:

tt (s): 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5

Measured hh (m): 8.7, 15.2, 18.9, 20.0, 18.5, 15.1, 8.9
a
Calculate the predicted height at each of the seven time values. [2]
b
Compute the absolute difference ∣predicted−measured∣|\text{predicted} - \text{measured}| for each time value, then calculate the mean absolute error (MAE). [2]
c
The launch team will trust the model for future predictions only if the MAE is less than 0.20 m. Advise the launch team whether the model should be used for future predictions, justifying your answer using your result from (b). [2]
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Solutions

4QuestionRange from graphsAssessment Practice
6 marks~9 minCriterion B
A sports analyst models the height (in metres) of a ball above the ground during a throw using functions of the form y=a(x−h)2+ky = a(x - h)^2 + k, where xx is horizontal distance (in metres).

Five functions are proposed:

y=x2y = x^2 \quad y=x2+3y = x^2 + 3 \quad y=(x−2)2y = (x-2)^2 \quad y=−x2+5y = -x^2 + 5 \quad y=−2(x+1)2−4y = -2(x+1)^2 - 4
a
Determine the range of each function. [3]
b
Analyse the five ranges to identify a pattern. State a general rule for the range of y=a(x−h)2+ky = a(x - h)^2 + k in terms of aa and kk, and explain why hh does not affect the range. [2]
c
The analyst claims any function with a<0a < 0 and k≤0k \leq 0 cannot model a ball thrown above the ground. Assess whether this claim is correct. [1]
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Solutions

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