P2 §2. Functions and graphs

Pure mathematics Year 2

Here's a short introduction to Pure maths 2 Chapter 2 Functions and graphs.

 

2.1 The modulus function: Understand and use the modulus function.

2.2 Functions and mappings: Understand mappings and functions, and use domain and range.

2.3 Composite functions: Combine two or more functions to make a composite function.

2.4 Inverse functions: Know how to find the inverse of a function graphically and algebraically.

2.5 y = |f(x)| and y = f(|x|): Sketch the graphs of the modulus functions y = |f(x)| and y = f(|x|).

2.6 Combining transformations: Apply a combination of two (or more) transformations to the same curve.

2.7 Solving modulus problems: Transform the modulus function.

2.8 Mixed exercise for chapter 2

2.9 Review exercise for chapter 2

 

Prior knowledge check

 

Q1. [GCSE Maths] Make $y$ the subject of each of the following:

(a) $ 5x = 9 - 7y $

(b) $ p = \frac{ 2y + 8x }{ 5 } $

(c) $ 5x - 8y = 4 + 9xy $

 

Answers:

(a) $ ... $

(b) $ ... $

(c) $ ... $

 

Q2. [GCSE Maths] Write each expression in its simplest form.

(a) $ ( 5x - 3 )^2 - 4 $

(b) $ \frac{ 1 }{ 2 (3x - 5) - 4 } $

(c) $ \frac{ \frac{ x + 4 }{ x + 2 } + 5 }{ \frac{ x + 4 }{ x + 2 } - 3 } $

 

Answers:

(a) $ ... $

(b) $ ... $

(c) $ ... $

 

Q3. [Pure maths 1] Sketch each of the following graphs. Label any points where the graph cuts the $x$- or $y$-axis.

(a) $ y = \textrm e^x $

(b) $ y = x ( x+4 ) ( x-5 ) $

(c) $ y = \sin x $, $ 0 \le x \le 360^\circ $

 

Answers:

(a) $ ... $

(b) $ ... $

(c) $ ... $

 

Q4. [Pure maths 1] $ \textrm f(x) = x^2 - 3x $. Find the values of:

(a) $ \textrm f(7) $

(b) $ \textrm f(3) $

(c) $ \textrm f(-3) $

 

Answers:

(a) $ ... $

(b) $ ... $

(c) $ ... $

 

Comment: Code breakers at Bletchley Park used inverse functions to decode enemy messages during World War II. When the enemy encoded a message they used a function. The code breakers' challenge was to find the inverse function that would decode the message.