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2: Functions
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Function Theory

Function Theory

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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

FUNCTION GRAPHS

Graph of a function

14:47

Finding function values from graph

15:35

Exercise

16:13

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

PROBLEM SOLVING SL+HL

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

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