Introduction to Functions
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Introduction to Functions — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionFunction notation f(x)Concept Practice
2 marks~3 minCriterion A
A structural engineer models the hypotenuse of a right-triangular roof truss using the function f(x)=3x+5f(x) = 3x + 5, where xx is a design parameter in metres and f(x)f(x) gives the hypotenuse length in centimetres. Building regulations require the hypotenuse to be no longer than 20 cm for this truss type.
a
Calculate f(4)f(4). [1]
b
Justify whether the truss meets the building regulation when x=4x = 4. [1]
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Solutions

2QuestionFunction notation f(x)Assessment Practice
2 marks~3 minCriterion D
A taxi company charges a base fare of 3.50 dollars and 2.10 dollars per kilometre. The total cost, in dollars, for a journey of dd kilometres is modelled by

C(d)=2.1d+3.5.C(d) = 2.1d + 3.5.

A passenger has a budget of exactly 20.00 dollars.
a
Calculate C(8)C(8). [1]
b
Justify whether the passenger can afford the 8 km journey, using both C(8)C(8) and C−1(20)C^{-1}(20) in your reasoning. [1]
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3QuestionRelation vs functionAssessment Practice
4 marks~6 minCriterion C
A parabolic solar reflector is designed so that its cross-section satisfies the relation x=y2−2x = y^2 - 2, where xx and yy are measured in metres.
a
Determine the domain and range of this relation. [2]
b
Explain whether this relation represents a function, using the vertical line test. [1]
c
A sensor must be placed at a unique horizontal position for each height yy. Justify whether the relation x=y2−2x = y^2 - 2, as stated, is suitable for this purpose, and state any restriction needed. [1]
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4QuestionFunction notation f(x)Assessment Practice
6 marks~9 minCriterion B
A computer network doubles its active nodes each cycle, modelled by f(x)=2x+1f(x) = 2x + 1, where one coordination node is added per cycle. Starting from a single seed node, the network state after each cycle is defined by a1=f(1)a_1 = f(1), a2=f(a1)a_2 = f(a_1), a3=f(a2)a_3 = f(a_2), and so on.
a
Calculate the values of a1a_1, a2a_2, a3a_3, and a4a_4. [2]
b
Deduce a general expression for ana_n in terms of nn. [2]
c
A network is considered stable once it exceeds 500 active nodes. Using your expression from part (b), justify whether the network reaches stability within 8 cycles. [2]

Solutions

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