Function Notation and Interpretation
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Function Notation and Interpretation — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionUsing Function Machines and DiagramsConcept Practice
2 marks~3 minCriterion A
A delivery company charges customers based on parcel weight. A function machine models the pricing structure:

Weight (kg)357
Charge (dollars)111927
a
Deduce the rule for this function machine, expressing your answer using correct function notation. [1]
b
The company states: "No parcel costing more than 35 dollars will be accepted." A customer has a parcel weighing 9 kg. Justify whether the company will accept this parcel. [1]
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Solutions

2QuestionDefining Piecewise and Step Functions IntroductoryAssessment Practice
3 marks~5 minCriterion C
A postal company charges for packages according to the step function shown in the graph below.

The cost (in dollars) remains constant within each weight interval and jumps at specific weight boundaries.
a
Explain what the open and closed circles at each boundary point on the graph indicate about which interval includes that boundary weight. [1]
b
Deduce the cost of posting a package weighing 3.5 kg. [1]
c
A customer has a budget of 9 dollars. Advise the customer whether this budget is sufficient to post a package weighing exactly 4 kg, and what weight limit they must stay within to achieve a lower cost. [1]
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Solutions

3QuestionUnderstanding Function Notation f of xAssessment Practice
4 marks~6 minCriterion D
A mobile phone carrier charges a flat monthly fee of 15 dollars plus 0.05 dollars per minute of talk time. The monthly cost in dollars is modelled by

C(m)=15+0.05mC(m) = 15 + 0.05m

where mm is the number of minutes used in a month.
a
Calculate C(200)C(200), the predicted monthly cost for a user who talks for 200 minutes. [1]
b
A second user budgets a maximum of 40 dollars per month. Determine the maximum number of minutes this user can talk without exceeding their budget. [1]
c
Advise the second user whether C(m)C(m) alone is sufficient for planning their monthly phone budget, referring to your result from part (b) and at least two limitations of the model. [2]
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Solutions

4QuestionUnderstanding Function Notation f of xAssessment Practice
6 marks~9 minCriterion B
A biologist models the growth of a bacterial colony. The population (in thousands) at each hourly stage is defined by a1=2a_1 = 2 and the recurrence relation an+1=f(an)a_{n+1} = f(a_n), where f(x)=3x−1f(x) = 3x - 1.

The first four hourly populations are:
a1=2a_1 = 2, a2=5a_2 = 5, a3=14a_3 = 14, a4=41a_4 = 41
a
Calculate f(f(f(2)))f(f(f(2))). [2]
b
Deduce a general formula for ana_n in terms of nn. [3]
c
The laboratory has capacity for 400 thousand bacteria. Using your formula from part (b), justify whether the laboratory capacity is exceeded at stage 6. [1]

Solutions

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