Introduction to Functions

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Introduction to Functions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionDefinition of a functionConcept Practice

2 marks~3 minCriterion C

A school nurse records the ages and heights of students in MYP 5. Two students are both 15 years old; one is 162 cm tall and the other is 178 cm tall.

Let

f: A \to H

represent the mapping from student age

a \in A

(years) to height

h \in H

(cm), where

A = \{14, 15, 16, 17, 18\}

and

H

is the set of plausible student heights in centimetres.

Justify whether

f

qualifies as a function, using the data above as evidence. [2]

Solutions

2QuestionEvaluating functionsAssessment Practice

2 marks~3 minCriterion D

A small business models its weekly production cost using

C(x) = 5x + 20

, where

x

is the number of items produced and

C(x)

is the cost in dollars.

Calculate

C(10)

and

C(25)

. [1]

The business considers scaling production to 1000 items per week. Justify whether the linear model

C(x) = 5x + 20

is a reliable predictor of costs at this scale. [1]

Solutions

3QuestionFunction notation f(x)Concept Practice

4 marks~6 minCriterion A

A city's temperature on a winter morning is modelled by the linear function

f(x)

, where

x

is the time in hours after midnight and

f(x)

is the temperature in °C. The graph of

f(x)

passes through

(-1, 4)

and

(3, -2)

Explain how to read

f(-1)

and

f(3)

directly from the graph, stating both values. [1]

Calculate

f(3) - f(-1)

. [1]

Interpret the value found in part (b) in the context of the temperature model, and justify whether the temperature is rising or falling over this time interval. [2]

Solutions

4QuestionFunction notation f(x)Assessment Practice

6 marks~9 minCriterion B

A mobile data plan charges a fixed monthly fee plus a constant rate per gigabyte (GB) used. Recorded charges are:

Data used (GB)	1	2	3	4	5
Monthly charge (dollars)	7	10	13	16	19

The total monthly charge is modelled by

f(x) = ax + b

, where

x

is the number of GB used.

Deduce the values of

a

and

b

, and hence state the formula for

f(x)

. [3]

The plan advertises a maximum possible charge of 40 dollars per month. Justify whether this claim is consistent with a customer who uses 12 GB. [2]

Interpret the meaning of

f(0)

in this context. [1]

Solutions

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