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Perplex
Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesCounting & BinomialsProof and Reasoning
Cartesian plane & linesQuadraticsFunction TheoryTransformations & asymptotes
2D & 3D GeometryTrig equations & identities
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random Variables
DifferentiationIntegration
Review VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex
IB Math AASL
/
Function Theory
/
Video
Edit

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 AASL
/
Function Theory
/
Video
Edit

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.

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

Existence of inverse function

1:11:35

Self-inverse functions

1:13:19

Finding inverse function with domain restriction

1:16:11

Exercise

1:18:14

Problem

1:26:01

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

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

Existence of inverse function

1:11:35

Self-inverse functions

1:13:19

Finding inverse function with domain restriction

1:16:11

Exercise

1:18:14

Problem

1:26:01

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