**All About Functions: O Level Math Exam Preparation Guide**

**What are Functions?**

A function relates an input to an output. In simple words, a function is a relationship between inputs where each input is related to **exactly one** output.

It is like a machine that has an input and an output.

And the function is the machine which determines the output.

**Before you read on, you might want to download this entire revision notes in PDF format to print it out, or to read it later. **

**This will be delivered to your email inbox.**

**How Does a Function Work?**

A function works as a relationship between the input and the output.

**Example of a function:**

*f(x) = 2x + 1*

The function *f* is the function name and the *x* inside the bracket is the input.

The *2x + 1* is the output.

So f(1) = 2(1) + 1 = 3

So 1 is the input and 3 is the output.

**Similarly…**

f(2) = 2(2) + 1 = 5

f(3) = 2(3) + 1 = 7

etc….

You must take note of something important:

Each input must only give **exactly one** output.

If an input gives 2 outputs, then it is NOT a function.

**Example of a non-function:**

*f(x)* = ± √x

In this case, an input of 4 will give 2 outputs which are ±2.

Therefore it is not a function.

You can refer to the diagram below for an easy reference of function and non-function.

## Types of Functions

### Linear Functions (*y *= m*x* + c, *x *= *a*, *y* = *b*) (Linear Equations)

*m* is the gradient and *c* is the y-intercept.

### Quadratic Functions of Different Forms (Quadratic Equations)

#### – y = ax^{2} + bx + c where a, b and c are constants and a ≠ 0

If *a* > 0, the graph has a minimum point

If *a* < 0, the graph has a maximum point

The graph of ax^{2} + bx + c has an axis of symmetry which passes through the minimum or maximum point.

#### – Completed the Square Form

To find the *x* – intercepts, let *y* = 0

To find the *y* – intercepts, let *x *= 0

The line of symmetry is *x* = *p*.

#### – Factorized Form

*x‒*intercepts are *x* = a and *x* = b

The line of symmetry of the graph in the form *x = (a +b)/2*

### Cubic Functions

### Reciprocal Functions

### Exponential Functions, y = a^{x}

### Logarithmic Functions (For A Maths Students)

__Note:__

__Note:__

· Point of intersection on *x*-axis: (1,0)

· Value of *x* is always positive.

· *y*-axis is the asymptote (a line that the graph of a function approaches but never touches).

· The graph approaches the *y*-axis but will never touch or intersect.

#### Special Case: Graph of y = lnx

__Note:__

*y = lnx*is the inverse of*y = e*.^{x}- the 2 graphs are a reflection along the line
*y = x.*

**Example of Function Question with Solutions**

The diagram shows the graph of *y = x ^{2} – x – 12*

- The graph cuts the
*y*-axis at C (0,*k*), write down the value of*k*. - The graph cuts the
*x*-axis at A and B, find the coordinates of A and B - Write down the equation of the line of symmetry
- Write down the coordinates of the minimum point of the curve.

### Solutions

## Last Minute Revision for O Level Math?

## Check out our exam guide on other topics here!

**Before you go, you might want to download this entire revision notes in PDF format to print it out, or to read it later. **

**This will be delivered to your email inbox.**

To Your Child’s Success,

Mr Tan Kok Heng

NIE Trained

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

**Does your child need help in his or her studies?**

**1) Live Zoom Lessons at Grade Solution Learning Centre**

At Grade Solution Learning Centre, we are a team of dedicated educators whose mission is to guide your child to academic success. Here are the services we provide:

– Live Zoom lessons

– EdaptIQ™, a smart learning platform that tracks your child’s progress, strengths and weaknesses through personalised digital worksheets.

– 24/7 Homework Helper Service

We provide all these services above at a very affordable monthly fee to allow as many students as possible to access such learning opportunities.

We specialise in English, Math, and Science subjects.

You can see our fees and schedules here >>

**2) Pre-recorded Online courses on Jimmymaths.com**

If you are looking for something that fits your budget, or prefer your child learn at his or her own pace, you can join our pre-recorded online Math courses.

Your child can:

– Learn from recorded videos

– Get access to lots of common exam questions to ensure sufficient practice

– Get unlimited support and homework help

You can see the available courses here >>