Do Now
• Determine the open intervals over which
the following function is increasing,
decreasing, or constant.
F(x) = | x + 1| + | x – 1|
• Determine whether the function is even,
odd, or neither. Why?
F(x) = x3 – 2x
P-9 Combinations of
Functions
Arithmetic Combinations of
Functions
• Just as 2 real numbers can be combined
by the operations of +, - ,X, ÷ to form other
real numbers, 2 functions can be
combined to create new functions.
Example
f(x) = 2x – 3
g(x) = x2 – 1
Find (f+g) x
x2 + 2x - 4
Find (f-g) x
-x2 + 2x - 2
Find (fg)x
Find f(x)
g(x)
x3 -3x2 + 2x - 3
2x - 3
x2 - 1
The domain of an arithmetic combination of functions f & g consists of
all real #’s that are common to the domain of f & g.
• f(x) = x2 + 3x
• g(x) = 3x – 7
Find (f+g)x
Find (f-g)x
Find (fg)x
Find f/g(x)
Composition of functions
• Another way of combining two functions is
to form the composition of one with the
other.
Written—
F(g(x)) or f ◦ g (x)
Example
• f(x) = x2
Find the f(g(x))
Find the g ◦ f (x)
g(x) = x + 1
(x + 1)2 = x2 + 2x + 1
x2 + 1
Homework
• Thursday HW– Page 104 (5-23 odd)
• Friday HW– Page 105 (31-45 odd)