part 1: combining functions graphically &...
TRANSCRIPT
Precalculus Name: 1.4 Function Composition Period: PART 1: COMBINING FUNCTIONS GRAPHICALLY & NUMERICALLY
( ) 2f x x ( ) 4g x x
The Algebraic rule for f(x) + g(x)
( ) ( ) 2 ( 4)f x g x x x
BIG IDEA!
The domain of the sum of two functions is:
Make a prediction! Domain of the difference of two functions:
x f(x)
-1
0
2
4.5
8
12.5
x g(x)
-1
0
2
4.5
8
12.5
Domain of f(x): Domain of g(x):
x f(x)+g(x)
-1
0
2
4.5
8
12.5
Domain of f(x)+ g(x):
PART 2: FUNCTION COMPOSITION
Composition f of g: ( )( )f g x
Composition g of f: ( )( )g f x
But what does it mean??
A few for practice …
1. If ( ) 2f x x and ( ) 4g x x ... evaluate:
a. ( ( ))f g x
b. ( ( ))g f x
2. If ( ) 3k x x and 2( )w x x …. evaluate:
a. ( )( )k w x
b. ( )( )w k x
Pick it up! Finding the domain of a composed function.
1. Compose the functions without simplifying the result. 2. Find the domain of the UNSIMPLIFIED composition as we have found domains in the past.
Give it a shot!
If 2( ) 1f x x and ( )g x x ….
FIRST! Evaluate:
a. ( ( ))f g x
b. ( ( ))g f x
THEN! Find the domain of:
a. ( ( ))f g x b. ( ( ))g f x