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Domain and Range of Functions — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionDetermining Domain and Range from GraphsConcept Practice
2 marks~3 minCriterion A
A drone follows a parabolic flight path over a restricted zone. Its horizontal position (in kilometres) is modelled by a continuous quadratic function, graphed with closed endpoints at and .
a
State the domain of the function in interval notation. [1]
b
The restricted zone spans km. Justify whether the drone's entire flight path lies within the restricted zone. [1]
Solutions
2QuestionIdentifying Domain and Range from TablesAssessment Practice
4 marks~6 minCriterion D
A biologist records the number of bacteria in a culture every hour for 10 hours.
Time (hours): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Population (thousands): 0.5, 0.8, 1.3, 2.1, 3.4, 5.5, 8.9, 14.4, 23.3, 37.7, 61.0
Time (hours): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Population (thousands): 0.5, 0.8, 1.3, 2.1, 3.4, 5.5, 8.9, 14.4, 23.3, 37.7, 61.0
a
State the domain of this model. [1]
b
State the range of this model. [1]
c
The biologist uses this model to predict the bacterial population at hours. Advise the biologist whether this prediction should be trusted, referring to the domain identified in part (a) and to the biological conditions of the culture. [2]
Solutions
3QuestionWriting Inequality Notation for Domain and RangeConcept Practice
2 marks~3 minCriterion B
A physiotherapist records a patient's pain score (on a scale of 1 to 11) during five consecutive daily sessions. The scores form the relation: .
a
Deduce the rule connecting the session number and the pain score . [1]
b
Express the domain and range of this relation using inequality notation. [1]
Solutions
4QuestionIdentifying 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
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