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 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: – x 2 – 18 = 0 – (x – 2)(2x + 3) = 0 – |x – 4| = 10 Using your calculator: – x 3 – 2x 2 + x – 1 = 0 – x 2 + 5x = 4 – 3x 3 – 25x + 8 = 0