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Perplex
Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesCounting & BinomialsProof and ReasoningComplex Numbers
Cartesian plane & linesQuadraticsFunction TheoryTransformations & asymptotesPolynomials
2D & 3D GeometryTrig equations & identitiesVectors
ProbabilityDescriptive StatisticsDistributions & Random Variables
DifferentiationIntegrationDifferential EquationsMaclaurin
Review VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex
IB Math AAHL
/
All units
/
Video

Video Review

Watch comprehensive review videos for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

IB Math AAHL
/
All units
/
Video

Video Review

Watch comprehensive review videos for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

Not your average video:

Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

Back

Function Theory

Video Review

Timeline

Function vs relation (vertical line test)

00:00

Evaluating functions

01:52

Exercise

02:15

Domain of a function

02:57

Range of a function

04:16

Notation for domain and range intervals

05:06

Exercise

06:41

Function as a model

10:18

Problem

11:38

FUNCTION GRAPHS

Graph of a function

14:47

Finding function values from graph

15:35

Graphing with technology

17:09

x-intercepts

17:44

y-intercepts

18:14

Exercise

19:12

Intersections with GDC

23:21

Exercise

24:04

Vertical asymptotes

26:30

Horizontal asymptotes

27:50

Exercise

28:56

Maxima and Minima

33:06

Exercise

34:18

COMPOSITE & INVERSE FUNCTIONS (SL +HL)

Composite functions

36:33

Exercise

37:59

Exercise

39:33

The identity function is \(\mathop{I}\left(x\right

40:32

Inverse applied to function is identity x

41:55

Finding inverse of specific value

42:14

Exercise

43:50

Exercise

44:39

Graphs of inverse functions

45:24

Exercise

47:13

Domain & range of inverse functions

48:03

Exercise

49:56

Finding inverse functions

51:29

Exercise

53:53

PROBLEM SOLVING SL+HL

Problem

55:27

Problem

58:41

Problem

1:02:35

HL ONLY

Even functions

1:07:48

Odd functions

1:08:23

Exercise

1:08:58

Existence of inverse function

1:11:35

Self-inverse functions

1:13:19

Exercise

1:14:27

Finding inverse function with domain restriction

1:16:11

Exercise

1:18:14

Problem

1:19:23

Problem

1:26:01

Problem

1:31:58

Problem

1:37:24

Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only

The video will automatically pause when it reaches a problem.

Function vs relation (vertical line test)

SL Core 2.2

A function is a rule that assigns to each number in its domain one number in its range. It is expressed in the form

​
f(x)=(some expression in x)
​

where ​f​ and ​x​ can be replaced by any letters.


A function is a special type of relation where each ​x​ value has only one possible ​y​-value.


For example, ​f(x)=3x2−2​ is a function, but ​x2+y2=1​ is not, since ​y=±√1−x2​​ has two possible values for each ​x.

Function vs relation (vertical line test)

SL Core 2.2

A function is a rule that assigns to each number in its domain one number in its range. It is expressed in the form

​
f(x)=(some expression in x)
​

where ​f​ and ​x​ can be replaced by any letters.


A function is a special type of relation where each ​x​ value has only one possible ​y​-value.


For example, ​f(x)=3x2−2​ is a function, but ​x2+y2=1​ is not, since ​y=±√1−x2​​ has two possible values for each ​x.

Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only
Back

Function Theory

Video Review

Timeline

Function vs relation (vertical line test)

00:00

Evaluating functions

01:52

Exercise

02:15

Domain of a function

02:57

Range of a function

04:16

Notation for domain and range intervals

05:06

Exercise

06:41

Function as a model

10:18

Problem

11:38

FUNCTION GRAPHS

Graph of a function

14:47

Finding function values from graph

15:35

Graphing with technology

17:09

x-intercepts

17:44

y-intercepts

18:14

Exercise

19:12

Intersections with GDC

23:21

Exercise

24:04

Vertical asymptotes

26:30

Horizontal asymptotes

27:50

Exercise

28:56

Maxima and Minima

33:06

Exercise

34:18

COMPOSITE & INVERSE FUNCTIONS (SL +HL)

Composite functions

36:33

Exercise

37:59

Exercise

39:33

The identity function is \(\mathop{I}\left(x\right

40:32

Inverse applied to function is identity x

41:55

Finding inverse of specific value

42:14

Exercise

43:50

Exercise

44:39

Graphs of inverse functions

45:24

Exercise

47:13

Domain & range of inverse functions

48:03

Exercise

49:56

Finding inverse functions

51:29

Exercise

53:53

PROBLEM SOLVING SL+HL

Problem

55:27

Problem

58:41

Problem

1:02:35

HL ONLY

Even functions

1:07:48

Odd functions

1:08:23

Exercise

1:08:58

Existence of inverse function

1:11:35

Self-inverse functions

1:13:19

Exercise

1:14:27

Finding inverse function with domain restriction

1:16:11

Exercise

1:18:14

Problem

1:19:23

Problem

1:26:01

Problem

1:31:58

Problem

1:37:24

Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only

The video will automatically pause when it reaches a problem.

Function vs relation (vertical line test)

SL Core 2.2

A function is a rule that assigns to each number in its domain one number in its range. It is expressed in the form

​
f(x)=(some expression in x)
​

where ​f​ and ​x​ can be replaced by any letters.


A function is a special type of relation where each ​x​ value has only one possible ​y​-value.


For example, ​f(x)=3x2−2​ is a function, but ​x2+y2=1​ is not, since ​y=±√1−x2​​ has two possible values for each ​x.

Function vs relation (vertical line test)

SL Core 2.2

A function is a rule that assigns to each number in its domain one number in its range. It is expressed in the form

​
f(x)=(some expression in x)
​

where ​f​ and ​x​ can be replaced by any letters.


A function is a special type of relation where each ​x​ value has only one possible ​y​-value.


For example, ​f(x)=3x2−2​ is a function, but ​x2+y2=1​ is not, since ​y=±√1−x2​​ has two possible values for each ​x.

Function graphsComposite & inverse functions (SL +HL)Problem Solving SL+HLHL only