Introduction to Functions
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Introduction to Functions — Free MYP4 Mathematics (Extended) 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

2QuestionRelation 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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3QuestionEvaluating functionsAssessment Practice
4 marks~6 minCriterion D
A mobile data plan charges a monthly fee. The total cost, in dollars, is modelled by f(x)=2x+1f(x) = 2x + 1, where xx is the number of gigabytes used.

The graph of ff is shown, with points marked at x=−1x = -1, x=0x = 0, and x=2x = 2.
a
State the coordinates of the three marked points. [1]
b
Show that f(4)=9f(4) = 9. [1]
c
Explain what f(4)=9f(4) = 9 means in this context, and justify whether the linear model is appropriate for this situation. [2]
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4QuestionDefinition of a functionAssessment Practice
6 marks~9 minCriterion B
A mobile data plan charges a fixed rate per gigabyte used. A network analyst records the following usage data for two customers.

Customer A
Input xx (GB used): 1, 2, 3, 41,\ 2,\ 3,\ 4
Output yy (cost in dollars): 3, 5, 7, 93,\ 5,\ 7,\ 9

Customer B
Input xx (GB used): 1, 1, 2, 31,\ 1,\ 2,\ 3
Output yy (cost in dollars): 3, 4, 5, 73,\ 4,\ 5,\ 7
a
Analyse the pattern in Customer A's data. Deduce a rule in the form y=f(x)y = f(x) and verify it using at least two input-output pairs. [3]
b
Evaluate whether the rule from part (a) applies to Customer B's data, supporting your reasoning with calculations. [1]
c
The analyst must decide whether to use a single function to model Customer B's pricing. Justify whether or not this is appropriate, and explain what this means for the reliability of the pricing model for Customer B. [2]

Solutions

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