Introduction to Functions

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Introduction to Functions — Free MYP5 Mathematics (Extended) 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

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

x

(GB used):

1,\ 2,\ 3,\ 4

Output

y

(cost in dollars):

3,\ 5,\ 7,\ 9

Customer B
Input

x

(GB used):

1,\ 1,\ 2,\ 3

Output

y

(cost in dollars):

3,\ 4,\ 5,\ 7

Analyse the pattern in Customer A's data. Deduce a rule in the form

y = f(x)

and verify it using at least two input-output pairs. [3]

Evaluate whether the rule from part (a) applies to Customer B's data, supporting your reasoning with calculations. [1]

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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