1. No category

Name: ____________________
Pre- Calculus 12
Date: _____________
Chapter 10 – Function Operations
10.1 – Sum and Differences of Functions
Recall: Function Notation and Operations
Evaluate the following expressions given the functions below:
g(x) = -3x + 1
h( x) 
f(x) = x2 + 7
12
x
a.
g(10) =
e.
b.
f(3) =
f.
c.
h(–2) =
g.
d.
j(5) =
h. Find x if f(x) = 23
j(x) = 2x
h(a) =
Find x if g(x) = 16
Find x if h(x) = –2
You can form new functions by performing operations
Sum of Functions h(x) = f(x) + g(x)
h(x) = (f+g)(x)
Difference of Functions h(x) = f(x) – g(x)
h(x) = (f-g)(x)
Example 1: Consider the functions f ( x)  2 x  1 and g ( x)  x 2 .
a) Determine the equation of the function h( x)  ( f  g )( x) .
b) Sketch the graph of h(x) – start with f(x) & g(x)!
Example 2: Consider the functions f ( x)  x  1 and g ( x)  x  2 .
a) Determine the equation of the function h( x)  ( f  g )( x) .
b) Sketch the graph of h(x).
c) State the domain of h(x), and use the graph to approximate the range of h(x).
Example 3:
Given the graphs of f(x) and g(x), sketch the graphs of
h( x)  ( f  g )( x) and
m( x)  ( f  g )( x) .
4
2
4
2
2
2
4
Example 4: Given f (x) = 3x2 + 2, g(x) = 4x, and h(x) = 7x - 1,
determine each combined function.
a) y = f (x) + g(x) + h(x)
Assignment: Page. 483 #1, 2, 5, 6, 8, 9a, 10ab, 11ab
b) y = f (x) + g(x) - h(x)
4