Functions - [Pure 3].

Question 1

What is the difference between the domain and range of a function?

Answer 1

The Domain is the set of x-values which satisfy a function and the Range is the set of y-values which satisfy a function.

Question 2

What does the ∈ symbol mean?

Answer 2

… is an element of.

(part of…)

Question 3

What does the ∉ symbol mean?

Answer 3

… not an element of.

(not part of…)

Question 4

What does the ℕ symbol mean?

Answer 4

the set of natural numbers.
{e.g. 1,2,3…}.

Question 5

What does the {x₁,x₂,…} mean?

Answer 5

the set with the elements x₁,x₂,…

Question 6

What does the {x: …} mean?

Answer 6

the set of all x such that…

Question 7

What does the ℤ symbol mean?

Answer 7

the set of integers.
{e.g. 0, ±1, ±2, ±3,…}.

Question 8

What does the ℤ⁺ symbol mean?

Answer 8

the set of positive integers.
{e.g. 1,2,3,…}.

Question 9

What does the ℤ⁺₀ symbol mean?

Answer 9

the set of non-negative integers (includes zero).
{e.g. 0,1,2,3,…}

Question 10

What does the ℝ symbol mean?

Answer 10

the set of real numbers.

Question 11

What does the ℚ symbol mean?

Answer 11

the set of rational numbers.
{e.g. p/q: p ∈ ℤ , q ∈ ℤ⁺}.

Question 12

What is interval notation?

Answer 12

The brackets that go around the interval (numbers contained within an interval). Use of square [ ] and curved ( ) brackets.

Question 13

Which brackets for Interval Notation do you use for a strict inequality?

Answer 13

Curved Brackets. ( )

Question 14

Which brackets for Interval Notation do you use for a non strict inequality (equal to aswell)?

Answer 14

Square Brackets. [ ]

Question 15

What interval notation would you give for a closed interval {x ∈ ℝ: a ≤ x ≤ b}.

Answer 15

[a , b].

Square Brackets on both sides.

Question 16

What interval notation would you give for the interval* {x ∈ ℝ: a ≤ x < b}.

Answer 16

[a , b).

Square on the left and curved on the right.

Question 17

What interval notation would you give for the interval* {x ∈ ℝ: a < x ≤ b}.

Answer 17

(a , b].

Curved on the left and square on the right.

Question 18

What interval notation would you give for an open interval {x ∈ ℝ: a < x < b}.

Answer 18

(a , b).

Curved Brackets on both sides.

Question 19

What is Mapping?

Answer 19

Inputting values and getting outputs. 1 input may lead to multiple outputs or multiple inputs may lead to 1 output.

Question 20

What is a function?

Answer 20

A type of mapping such that every element of the domain is mapped to exactly 1 element in the range. (leads to 1 output from 1 or multiple inputs).

Question 21

What is a 1-to-1 function?

Answer 21

1 input to a function leads to 1 output.
[f(0) = -1, f(1) = 1].

Question 22

What is a Many-to-1 function?

Answer 22

Multiple inputs lead to the same 1 output.
[e.g f(2) = 4, f(-2) = 4].

Question 23

What is 1-to-many mapping?

Answer 23

Each input has more than 1 different output.
[f(4) = ±2].

Question 24

What is a compostite function?

Answer 24

Combined functions such as fg(x) or ba(x). You sub one function into the other.

Generally fg(x) ≠ gf(x).

Question 25

How do you know which one to sub into the other for a composite function?

Answer 25

The **one on the inside** (e.g. f**g**(x) the 'g(x)', you sub into the other 'f(x)').

Question 26

What is a ***Inverse* function?**

Answer 26

It **reverses the effect of a function** and does the opposite of the original function. You write it as **f ^-1(x).**

Question 27

What is the *only type of function* which **has an inverse?**

Answer 27

Only **1-to-1** functions.

Question 28

What is the **Inverse** of the **Domain of f(x)?**

Answer 28

The **Range** of the **Inverse** [f ^-1(x)].

Question 29

What is the **Inverse** of the **Range of f(x)?**

Answer 29

The **Domain** of the **Inverse** [f ^-1(x)].

Question 30

What is it called if you have a **function where f(x) and f^-1(x) are the same?**

Answer 30

A **Self-Inverse** Function.

Question 31

For **Transformations**, what **Acronym** can be used to remember whether stretch or translate comes first Vertically and Horizontally?

Answer 31

**- VAST THITTS -** * * *Vertical* - Always **Stretch, then Translate.** * *Horizontal* - Its **Translate then Stretch.**

Question 32

What is **restricting the Domain?**

Answer 32

**Shortening the x-values** so it isnt infinite. ## Footnote It can make 1-to-many functions which dont have an inverse, have an inverse when restricted.