You're viewing 4 free preview questions for Maths AA SL — subscribe to unlock 243 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Functions and Their Properties · Paper 1 — Free Maths AA SL Practice Questions

1FoundationSAQ-SDefinition and types of functions (one-to-one, onto etc.)s8 marksPaper 1~12 min

A function

f

is defined by

f(x) = \dfrac{2x + 3}{x - 1}

, for

x \in \mathbb{R},\ x \neq 1

(a)

State the equation of the horizontal asymptote of

f

. [1 mark]

(b)

Show that

f(a) = f(b) \Rightarrow a = b

, and hence state whether

f

is a one-to-one function. [3 marks]

(c)

Write down the range of

f

. [1 mark]

(d)

Find

f^{-1}(x)

, stating its domain. [3 marks]

Solutions

2FoundationSAQ-SDefinition and types of functions (one-to-one, onto etc.)s5 marksPaper 1~8 min

Consider the function

g: \mathbb{R} \to \mathbb{R}

defined by

g(x) = x^3 - 4x

(a)

State what it means for a function

f: A \to B

to be onto (surjective). [1 mark]

(b)

Show that

g

is onto. [2 marks]

(c)

The codomain of

g

is now restricted to

[0, +\infty)

, giving

h: D \to [0, +\infty)

where

h(x) = x^3 - 4x

and

D \subseteq \mathbb{R}

. Find the smallest domain

D

such that

h

is onto

[0, +\infty)

. [2 marks]

Solutions

3MasterySAQ-SDefinition and types of functions (one-to-one, onto etc.)s5 marksPaper 1~8 min

A function

g

is defined by

g(x) = x^2 - 4x + 5

, for

x \geq 2

x \in \mathbb{R}

(a)

Show that

g

is strictly increasing on its domain, and hence that

g

is a one-to-one function. [3 marks]

(b)

Hence find the range of

g

. [2 marks]

Solutions

4ChallengeSAQ-LDefinition and types of functions (one-to-one, onto etc.)s5 marksPaper 1~8 min

Consider the function

f: \mathbb{R} \setminus \{1\} \to \mathbb{R}

defined by

f(x) = \dfrac{2x + 3}{x - 1}

. - A function

f: A \to B

is one-to-one if

f(a) = f(b) \Rightarrow a = b

for all

a, b \in A

. - A function

f: A \to B

is onto if for every

y \in B

, there exists

x \in A

such that

f(x) = y

(a)

Justify algebraically that

f

is a one-to-one function. [4 marks]

(b)

(i) Show that the range of

f

\mathbb{R} \setminus \{2\}

. [3]
(ii) Hence determine, with justification, whether

f

is an onto function. [1 mark]

Solutions

Questions 5-247

Unlock these questions with Premium

That's every free question here — 4 of 247.

+243 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade