Domain and Range of Functions
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Domain and Range of Functions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionWriting Inequality Notation for Domain and RangeConcept Practice
2 marks~3 minCriterion A
A drone delivery service operates along a straight route. Its altitude function f(x)f(x) is graphed below, where xx represents horizontal distance (km) from the depot.

The graph shows an open circle at x=−3x = -3 and a closed circle at x=5x = 5.

Write the domain of ff using inequality notation. [2]
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Solutions

2QuestionWriting Inequality Notation for Domain and RangeAssessment Practice
4 marks~6 minCriterion C
A piecewise function f(x)f(x) is defined by:

f(x)={x2−4,x<1−13x−23,1≤x≤4f(x) = \begin{cases} x^2 - 4, & x < 1 \\ -\dfrac{1}{3}x - \dfrac{2}{3}, & 1 \leq x \leq 4 \end{cases}

The parabolic piece has an open circle at (1, −3)(1,\ -3); the linear piece has closed circles at (1, −1)(1,\ -1) and (4, −2)(4,\ -2).
a
Write the domain of f(x)f(x) in inequality notation. [1]
b
Justify why x=1x = 1 is included in the domain of f(x)f(x), despite the open circle on the parabolic piece. [1]
c
A student claims: "Because f(x)f(x) is discontinuous at x=1x = 1, the point x=1x = 1 must be excluded from the domain." Critique this claim, using the left-hand limit and the value of f(1)f(1) to support your reasoning. [2]
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Solutions

3QuestionIdentifying Domain and Range from TablesAssessment Practice
6 marks~9 minCriterion D
A city's water treatment plant records incoming flow rate (in m3/h\text{m}^3/\text{h}) every hour for 24 hours.

Hour: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Flow (m3/h\text{m}^3/\text{h}): 120, 115, 130, 145, 160, 180, 200, 210, ?, ?, ?, 195, 170, 155, 140, 130, 125, 135, 150, 170, 190, 185, 160, 140
a
State the domain of the function represented by the valid readings only. Write your answer in set notation. [2]
b
Deduce the range of the flow rates using the valid readings only. Write your answer in set notation. [2]
c
Advise the plant operators whether the incomplete data are sufficient to plan for peak demand. In your response:
— identify which hours are missing and explain why they are significant for peak demand;
— state one assumption needed to estimate the missing values and evaluate how that assumption affects the reliability of capacity planning. [2]
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Solutions

4QuestionIdentifying Discrete and Continuous FunctionsAssessment Practice
4 marks~6 minCriterion B
A mobile data analyst records the number of text messages sent per hour during a network stress test:

hh (hour): 1, 2, 3, 41, \ 2, \ 3, \ 4
mm (messages): 5, 8, 13, 205, \ 8, \ 13, \ 20
a
Calculate the next three terms of the sequence. [1]
b
Deduce a formula for mm in terms of hh that fits all given data points. [2]
c
The analyst proposes using this model to predict message counts at non-integer hours such as h=1.5h = 1.5. Advise the analyst whether this proposal is appropriate, justifying your answer with reference to the domain of the function. [1]

Solutions

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