1.6 Operations on Functions and Composition of Functions

• Pg. 73 # 132 – 137 Pg. 67 # 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.– 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 fog D: (-∞, 1)U(1, ∞ )

R: (-1, ∞)gof D: (- ∞ , -√2)U

(-√2, √2)U(√2, ∞ ) R: (- ∞, 0)U(0, ∞)

• #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, ∞)

#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 thef◦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:

– x2 – 18 = 0– (x – 2)(2x + 3) = 0– |x – 4| = 10

• Using your calculator:– x3 – 2x2 + x – 1 = 0– x2 + 5x = 4– 3x3 – 25x + 8 = 0