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Domain and Range of Functions — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionApplications in Real-World GraphsConcept Practice
2 marks~3 minCriterion A
The graph below shows the height (in metres) of a ball thrown vertically upward as a function of time (in seconds). The ball is released from ground level, reaches a maximum height of m at s, and returns to the ground at s.
a
State the domain and range of this function using interval notation. [1]
b
The ball must clear a barrier of height m. Using the graph, identify the interval of time during which the ball is above m, and justify whether the ball successfully clears the barrier. [1]
Solutions
2QuestionIdentifying Discrete and Continuous FunctionsAssessment Practice
4 marks~6 minCriterion C
A museum records two data sets over six hours: the number of visitors counted each hour (whole numbers only) and the water temperature in an aquarium tank measured continuously.
Visitor counts (hours 1–6): 15, 22, 18, 27, 20, 24.
Water temperature (°C): recorded at every instant throughout the six hours.
Visitor counts (hours 1–6): 15, 22, 18, 27, 20, 24.
Water temperature (°C): recorded at every instant throughout the six hours.
a
State which data set represents a discrete function and which represents a continuous function. [1]
b
Calculate the range of the visitor counts over the six hours. [1]
c
The museum manager claims the aquarium temperature data is more useful than the visitor counts for detecting sudden environmental changes. Justify this claim using the mathematical properties of continuous and discrete functions. [2]
Solutions
3QuestionIdentifying Domain and Range from TablesConcept Practice
2 marks~3 minCriterion B
A delivery drone records the following data during a test flight:
Time, (minutes):
Distance from base, (metres):
Time, (minutes):
Distance from base, (metres):
a
State the domain and range of the function represented by this data. [1]
b
The drone's safe operating limit is a maximum distance of 8 metres from base. Using the rule relating to , justify whether the drone exceeds this limit during the flight. [1]
Solutions
4QuestionIdentifying Domain and Range from TablesAssessment Practice
6 marks~9 minCriterion D
A wildlife park has a daily water supply of 5000 litres. Its largest enclosure (Enclosure A) must receive at least 200 litres per day. Daily water consumption (in litres) for three enclosures over one week is recorded below.
| Day | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|---|---|---|---|---|---|---|---|
| Enclosure A (L) | 1200 | 1300 | 1250 | 1400 | 1350 | 1500 | 1450 |
| Enclosure B (L) | 800 | 750 | 900 | 850 | 700 | 950 | 1000 |
| Enclosure C (L) | 600 | 650 | 550 | 700 | 600 | 750 | 800 |
a
State the domain and calculate the range of the function representing total daily water consumption across all three enclosures. [2]
b
Deduce whether the park's weekly schedule is feasible under both the 5000-litre supply constraint and the 200-litre minimum for Enclosure A. Support your answer with calculations. [2]
c
Justify whether the constant daily-value model provides a reliable basis for the park's water management decisions, identifying two real-world factors that affect your judgement. [2]
Solutions
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