1.6 Operations on Functions and
Composition of Functions
• Pg. 73
Pg. 67
# 132 – 137
# 8 – 18 even, 43 – 46 all, 67
• A school club buys a scientific calculator for
$18.25 to use as a raffle prize. The club charges
$0.50/ticket.
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Write an equation of the club’s profit.
Graph your equation.
Find the domain and range.
How many tickets must be sold to realize a profit?
1.6 Operations on Functions and
Composition of Functions
Pg. 66 Problems
•
#13
•
#15 fog D: [-1, ∞ )
R: [-2, ∞ )
gof D: (- ∞ , -1]U[1, ∞ )
R: [0, ∞)
•
#17 fog D: [-2, ∞ )
R: [-3, ∞ )
gof D: (- ∞ , -1]U[1, ∞ )
R: [0, ∞)
fog D: (-∞, 1)U(1, ∞ )
R: (-1, ∞)
gof D: (- ∞ , -√2)U
(-√2, √2)U(√2, ∞ )
R: (- ∞, 0)U(0, ∞)
#39 – 42
• #39 – same graph shifted up
one
• #40 – same graph shifted
down 2
• #41 – graph stretched by 2
• #42 – graph reflected about
the x – axis and then
stretched 2
1.6 Operations on Functions and
Composition of Functions
Composition Effects on
Transformations and Reflections
• Depending on what you are
composing, you could just
be creating a shift or
reflection of a function.
• Look at what is inside the
f◦g(x) to see if anything
could transpire before you
would consider graphing
the new function.
Balloon Fun!! 
• A spherically shaped
balloon is being inflated so
that the radius r is changing
at the constant rate of 2
in./sec. Assume that r = 0 at
time t = 0. Find an algebraic
representation V(t) for the
volume as a function of t
and determine the volume
of the balloon after 5
seconds.
1.6 Operations on Functions and
Composition of Functions
Shadow Movement
• Anita is 5 ft tall and walks at
the rate of 4 ft/sec away
from a street light with it’s
lamp 12 ft above ground
level. Find an algebraic
representation for the
length of Anita’s shadow as
a function of time t, and
find the length of the
shadow after 7 sec.
More Rectangles!!
• The initial dimensions of a
rectangle are 3 by 4 cm, and
the length and width of the
rectangle are increasing at
the rate of 1 cm/sec. How
long will it take for the area
to be at least 10 times its
initial size?
2.1 Zeros of Polynomial Functions
Polynomial Functions
• What is a polynomial
function?
• What is a zero?
• How can you tell the max
number of zeros from a
polynomial function?
Find the zeros…
• Algebraically:
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x2 – 18 = 0
(x – 2)(2x + 3) = 0
|x – 4| = 10
• Using your calculator:
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x3 – 2x2 + x – 1 = 0
x2 + 5x = 4
3x3 – 25x + 8 = 0