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2: Functions
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Function Theory

Function Theory

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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 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 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