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

1QuestionWriting 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: (1,11), (2,9), (3,7), (4,5), (5,3)(1, 11),\ (2, 9),\ (3, 7),\ (4, 5),\ (5, 3).
a
Deduce the rule connecting the session number xx and the pain score yy. [1]
b
Express the domain and range of this relation using inequality notation. [1]

Solutions

2QuestionApplications in Real-World GraphsAssessment Practice
2 marks~3 minCriterion D
A ball is thrown vertically upward from a rooftop. Its height above the ground, hh metres, is modelled by h(t)=−5t2+20t+15h(t) = -5t^2 + 20t + 15, where tt is the time in seconds after release. A safety regulation states that any object above 30 metres poses a risk to overhead cables.

Justify whether the ball breaches the safety regulation of 30 metres, using the function to support your conclusion. [2]
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Solutions

3QuestionWriting 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

4QuestionIdentifying Domain and Range from TablesAssessment Practice
6 marks~9 minCriterion A
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

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