Function Notation and Interpretation
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Function Notation and Interpretation — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionDefining Piecewise and Step Functions IntroductoryAssessment Practice
2 marks~3 minCriterion A
A delivery drone travels along a straight route. Its speed vv (in m/s) over time tt (in seconds) is modelled by the graph shown.

The graph shows:
- a horizontal segment from t=0t = 0 to t=4t = 4 at v=3v = 3
- a segment with slope 22 from (4, 3)(4,\ 3) to (8, 11)(8,\ 11)

Construct the piecewise function v(t)v(t) using correct mathematical notation. [2]
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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
6 marks~9 minCriterion D
A civil engineer models the cost, in thousands of dollars, of a concrete beam of length xx metres using f(x)=1.2x+50f(x) = 1.2x + 50. A 15% safety surcharge gives the total cost function g(f(x))=1.15 f(x)g(f(x)) = 1.15\, f(x).

The measured length of a beam is 12 metres, with a possible error of ±0.5\pm 0.5 metres.
a
Calculate g(f(11.5))g(f(11.5)) and g(f(12.5))g(f(12.5)) to determine the range of total costs for this beam. [2]
b
Deduce whether the linear model f(x)f(x) remains appropriate when x=100x = 100 metres, referring to how material and structural behaviour affect costs at large beam lengths. [2]
c
The company must submit a single fixed-cost bid for this beam. Advise the engineer which value to bid, justifying your recommendation using the range found in part (a) and the financial consequence of the alternative choice. [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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