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1.6 Operations on Functions and Composition of Functions

1.6 Operations on Functions and Composition of Functions. Pg. 73 # 132 – 137 Pg. 67 # 8 – 18 even, 43 – 46 all, 67 #121 2 L + 440 #122 l = 125, A = 125 w #123 t = 6.16 hrs #124 r = 6.91 units #125 P ( n ) = 0.50 n – 18.25 #126 Graph

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1.6 Operations on Functions and Composition of Functions

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  1. 1.6 Operations on Functions and Composition of Functions • Pg. 73 # 132 – 137 Pg. 67 # 8 – 18 even, 43 – 46 all, 67 • #121 2L + 440 #122 l = 125, A = 125w • #123 t = 6.16 hrs #124 r = 6.91 units • #125 P(n) = 0.50n – 18.25 #126 Graph • #127 D: {0,1,2…} R: {-18.25, -17.75, -17.25,…} • #128 37 tickets #9 (f ◦ g)(3) = 8; (g ◦ f)(-2) = 3 • #11 (f ◦ g)(3) = 9; (g ◦ f)(-2) = 66 • #13 (f ◦ g)(x): D:(-∞,1)U(1,∞) R:(-1,∞); (g ◦ f)(x): D:(-∞,-√2)U(-√2,√2)U(√2,∞) R:(-∞,0)U(0,∞) • #15 (f ◦ g)(x): D:[1,∞) R:[-2,∞); (g ◦ f)(x): D:(-∞,-1]U[1,∞) R:[0,∞) • #17 (f ◦ g)(x): D:[-2,∞) R:[-3,∞); (g ◦ f)(x): D:(-∞,-1]U[1,∞) R:[0,∞) • #19 Show Quadratic Formula • #39 Graph #40 Graph #41 Graph #42 Graph

  2. 1.6 Operations on Functions and Composition of Functions • A school club buys an iPhone for $200 to use as a raffle prize. The club charges $5.00/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?

  3. 1.6 Operations on Functions and Composition of Functions Composition Effects on Transformations and Reflections Balloon Fun!! A spherically shaped balloon is being inflated so that the radius r is changing at the constant rate of 3.5 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 4 seconds. • 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.

  4. 1.6 Operations on Functions and Composition of Functions Shadow Movement 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? • Sally 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 Sally’s shadow as a function of time t, and find the length of the shadow after 7 sec.

  5. 2.1 Zeros of Polynomial Functions Polynomial Functions 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 • What is a polynomial function? • What is a zero? • How can you tell the max number of zeros from a polynomial function?

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