A2 Functions

Question 1

Domain

Answer 1

The set of possible inputs (x values) for a function

Question 2

Range

Answer 2

The set of possible outputs (y values) for a function

Question 3

Types of function mappings

Answer 3

• One to one
• One to many
• Many to one
• Many to many

Question 4

One to one mapping

Answer 4

Each input is mapped to exactly one input

Question 5

One to many mapping

Answer 5

Each input may be mapped to two or more outputs

Question 6

Many to one mapping

Answer 6

Two or more inputs may be mapped to the same output

Question 7

Many to many mapping

Answer 7

Two or more inputs may be mapped to two or more outputs.

Question 8

Define a ‘function’

Answer 8

A mapping where every input has exactly one output. Multiple inputs can have the same output.

Question 9

When does the order of translations matter?

Answer 9

The order matters if the transformations are a stretch and a translation in the same direction.

Question 10

What do you do if a many to one function’s inverse isn’t a function?

Answer 10

• Restrict the domain of the many to one function to turn in into a one to one function.
• This means the inverse function will also be a function.

Question 11

On a graph, what represents the domain and the range?

Answer 11

X value is the domain
Y value is the range

Question 12

How do you find the range of a function?

Answer 12

• Find the domain of its inverse function. That is the range of your function.

Question 13

What does |f(x)| do to a graph, e.g. sin x?

Answer 13

It means y values can no longer be negative. Any lines that cross the X axis are reflected perfectly back upward.

Question 14

What does f(|x|) do to a graph, e.g. sin x?

Answer 14

It means negative values of x can no longer be inputted, so the part of the graph where x < 0, is reflected in the Y axis.

Question 15

How to solve inequalities like:
|x + 4 | ≤ |x + 1|

Answer 15

Draw them out, then find the area that |x + 1| is above |x+4| (y axis), and that is your region.