functions
TRANSCRIPT
Block 3
Functions
What is to be Learned?
• What a function is• Different ways functions can be represented• Meaning of words domain and range• How to express functions
Functions are like Factories
Basic Function
Something goes in and comes out different (usually!)
In Out+ 4Domain Range
Basic Function
Something goes in and comes out different (usually!)
In Out+ 4Domain Range
Basic Function
In Out 5 -5 x
In Out+ 4
9-1
x + 4
Basic Function
Domain Range 5 -5 x
In Out+ 4
9-1
x + 4
Fancy Way of Writing
F(x) = x + 4 ↑ ↑ Domain Range F(7) ? F(7) = 7 + 4= 11
F of x
F(x) = 2x + 3 Domain { 1 , 3 , 5 }
Range?F(1)?F(1) = 2(1) + 3 = 5F(3) = 9F(5) = 13
Range { 5 , 9 , 13 }
Representing Functions
Table
X 1 2 3 4 5
F(x) 5 7 9 11 13
F(x) = 2x + 3
Graph
x
F(x)
just like Y
f(x) = 2x + 3
Daft looking things
Domain Range
5 13
10 2311 2519 41
f(x) = 2x + 3
Definition
For every value of x in the domain, there is exactly one value of f (or y) in the range
Domain Range
f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
f(x) = 5x + 9 f(x + 3)?
f(x + 3) =
= 5x + 15 + 9 = 5x + 24
5 + 9x + 3( )x
f(x) = 3x – 2
f(x + 5) = 3 = 3x + 15 – 2 = 3x + 13
– 2 x + 5( )
f(x + 5)?
f(x) = x2
f(x + 3) =
= (x + 3)(x + 3) = x2 + 3x + 3x + 9 = x2 + 6x + 9
2x + 3( )
f(x + 3)?
Functions
In functions the domain values (usually x) give one range value (usually f(x) or y)
Can be represented by formulae, graphs, tables or daft diagrams.
f(x) = x2 + 6f(4) =
f(x + 3) = 42 + 6(x + 3)2 + 6
g(x) = x2 + 4x – 3g(5) =
g(x – 7 ) = 52 + 4(5) – 3(x – 7)2 + 4(x – 7) – 3
f(x) = 6x – 2
f(x + 4) = 6 = 6x + 24 – 2 = 6x + 22
– 2 x + 4( )
f(x + 4)?Key Question
Forbidden Domain Values!
Sums that do not work!!!!!
• Dividing by zero• Square root of a negative
Applying to Functions
f(x) = 10/x
Domain: x cannot equal zero
x = 0
f(x) = √xDomain: x must not be negative
x ≥ 0
Sneakier
f(x) = 10/x-3
Domain: x = 3
f(x) = √x – 5 Domain x ≥ 5
For some functions there are domain values which are undefined
Ex f(x) = √x – 7Domain x ≥ 7