Functions - [Pure 3]. Flashcards
What is the difference between the domain and range of a function?
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.
What does the ∈ symbol mean?
… is an element of.
(part of…)
What does the ∉ symbol mean?
… not an element of.
(not part of…)
What does the ℕ symbol mean?
the set of natural numbers.
{e.g. 1,2,3…}.
What does the {x1,x2,…} mean?
the set with the elements x1,x2,…
What does the {x: …} mean?
the set of all x such that…
What does the ℤ symbol mean?
the set of integers.
{e.g. 0, ±1, ±2, ±3,…}.
What does the ℤ+ symbol mean?
the set of positive integers.
{e.g. 1,2,3,…}.
What does the ℤ+0 symbol mean?
the set of non-negative integers (includes zero).
{e.g. 0,1,2,3,…}
What does the ℝ symbol mean?
the set of real numbers.
What does the ℚ symbol mean?
the set of rational numbers.
{e.g. p/q: p ∈ ℤ , q ∈ ℤ+}.
What is interval notation?
The brackets that go around the interval (numbers contained within an interval). Use of square [ ] and curved ( ) brackets.
Which brackets for Interval Notation do you use for a strict inequality?
Curved Brackets. ( )
Which brackets for Interval Notation do you use for a non strict inequality (equal to aswell)?
Square Brackets. [ ]
What interval notation would you give for a closed interval {x ∈ ℝ: a ≤ x ≤ b}.
[a , b].
Square Brackets on both sides.
What interval notation would you give for the interval* {x ∈ ℝ: a ≤ x < b}.
[a , b).
Square on the left and curved on the right.
What interval notation would you give for the interval* {x ∈ ℝ: a < x ≤ b}.
(a , b].
Curved on the left and square on the right.
What interval notation would you give for an open interval {x ∈ ℝ: a < x < b}.
(a , b).
Curved Brackets on both sides.
What is Mapping?
Inputting values and getting outputs. 1 input may lead to multiple outputs or multiple inputs may lead to 1 output.
What is a function?
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).
What is a 1-to-1 function?
1 input to a function leads to 1 output.
[f(0) = -1, f(1) = 1].
What is a Many-to-1 function?
Multiple inputs lead to the same 1 output.
[e.g f(2) = 4, f(-2) = 4].
What is 1-to-many mapping?
Each input has more than 1 different output.
[f(4) = ±2].
What is a compostite function?
Combined functions such as fg(x) or ba(x). You sub one function into the other.
Generally fg(x) ≠ gf(x).
How do you know which one to sub into the other for a composite function?
The one on the inside (e.g. fg(x) the ‘g(x)’, you sub into the other ‘f(x)’).
What is a Inverse function?
It reverses the effect of a function and does the opposite of the original function. You write it as f -1(x).
What is the only type of function which has an inverse?
Only 1-to-1 functions.
What is the Inverse of the Domain of f(x)?
The Range of the Inverse [f -1(x)].
What is the Inverse of the Range of f(x)?
The Domain of the Inverse [f -1(x)].
What is it called if you have a function where f(x) and f-1(x) are the same?
A Self-Inverse Function.
For Transformations, what Acronym can be used to remember whether stretch or translate comes first Vertically and Horizontally?
- VAST THITTS -
* * Vertical - Always Stretch, then Translate.
* Horizontal - Its Translate then Stretch.
What is restricting the Domain?
Shortening the x-values so it isnt infinite.
It can make 1-to-many functions which dont have an inverse, have an inverse when restricted.
