Types of Functions
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Types of Functions — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionLinear functionsConcept Practice
4 marks~6 minCriterion A
A cyclist's journey is shown on the distance–time graph below. The two labelled points are (1,15)(1, 15) and (3,45)(3, 45), where the horizontal axis shows time in hours and the vertical axis shows distance in kilometres.
a
Interpret what the gradient of the line represents in the context of this journey. [1]
b
Calculate the cyclist's speed in km/h. [1]
c
A cycling event requires competitors to cover at least 40 km in the first 2.5 hours. Justify whether this cyclist meets that requirement. [2]
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2QuestionIdentify from equationsAssessment Practice
4 marks~6 minCriterion B
A landscape architect is designing square garden plots. Each plot has a side length of xx cm, and the usable planting area yy cm² follows the pattern below.

xx (cm): 1, 2, 3, 41, \ 2, \ 3, \ 4
yy (cm²): 3, 7, 13, 213, \ 7, \ 13, \ 21
a
Calculate the first differences and second differences for the yy-values. [2]
b
Deduce the type of function (linear or quadratic) that models this data, justifying your answer using the differences found in part (a). [1]
c
The architect needs the usable planting area to exceed 90 cm². Advise the architect whether a plot with side length x=6x = 6 cm is sufficient to meet this requirement. [1]
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3QuestionIdentify from graphsAssessment Practice
4 marks~6 minCriterion C
The graph shows a smooth curve with a local maximum at approximately (−1, 4)(-1,\ 4) and a local minimum at approximately (2, −3)(2,\ -3). The curve falls without bound to the left and rises without bound to the right.
a
Identify the type and degree of the function shown. [1]
b
Deduce the end behaviour of the function, expressing your answer using limit notation as x→+∞x \to +\infty and as x→−∞x \to -\infty. [1]
c
A civil engineer models the cross-section of a valley using this function. She needs the model to capture both a ridge and a trough within the domain. Critique the suggestion that a quadratic function would serve as an equally valid model, using the turning points of the graph as evidence. [2]
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4QuestionRational functionsAssessment Practice
4 marks~6 minCriterion D
A patient receives a single oral dose of medication. The concentration C(t)C(t) of the drug in the bloodstream (in mg/L), tt hours after ingestion, is modelled by

C(t)=20tt2+4.C(t) = \frac{20t}{t^2 + 4}.
a
Calculate C(2)C(2). Show all working and state your answer in mg/L. [1]
b
Calculate C(6)C(6). Show all working and state your answer in mg/L. [1]
c
The function has a horizontal asymptote at C=0C = 0. Critique the use of this model as a reliable representation of drug elimination for an actual patient. [2]
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