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Functions and Their Properties · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SDefinition and types of functions (one-to-one, onto etc.)6 marksPaper 2~9 min

A small independent bookstore tracks the number of customers,

C

, each day. The owner models the number of customers by

C(t) = at^2 + bt + c

, where

t

is the number of hours after opening,

0 \leq t \leq 10

. The following data are recorded:

t

(hours) —

C

(customers)

0

—

5

2

—

21

5

—

75

(a)

Show that

C(t) = 2t^2 + 4t + 5

. [3 marks]

(b)

Determine whether

C(t)

is one-to-one on the domain

0 \leq t \leq 10

. Justify your answer using the vertex of the parabola and the behaviour of the function the domain. [3 marks]

Solutions

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