Algebra 2/Trig
Name: __________________________________
Section 2.4 Notes: Operations with Functions p. 111
Goals: Add, subtract, multiply and divide functions. Find the restrictions on the domain when dividing.
ADDITION OF FUNCTIONS
SUBTRACTION OF FUNCTIONS
MULTIPLICATION OF FUNCTIONS
DIVISION OF FUNCTIONS
When we divide functions we must state the restrictions for the Domain. We are looking for the values of x that
make the denominator equal to zero.
Homework (Part 1): Page 115 #12 – 34 ALL.
Composition of Functions p. 111
SQUARING A BINOMIAL
Example:
does NOT equal
We could FOIL, but here is a shortcut.
3 STEPS:
1. Square the ___________________ term.
2. Multiply the ____________________ together and __________________ it.
3. Square the _______________ term.
Example 1:
Step 1:
Step 2:
Step 3:
Put it all together: _____________________________________________
Example 2:
COMPOSITION OF FUNCTIONS
Example 3: f(x) = 4x; g(x) = x - 5
You Try: Find g o f
Example 4: Evaluate (f o g)(6) when f(x) = 4x and g(x) = x – 5
There are 2 ways to do this:
Option 1:
Option 2:
Example 5: f(x) = x2 – 1; g(x) = 2x + 2
Find f o g
Find g o f
Checkpoint: Using the functions from the above example, find: 1. f o g (0)
Homework: Pages 115 & 116: 35 – 58 ALL, 60 – 61 and 63.
2. f o g (-2)
3. f o g (3)