1. 1.6 Operations on Functions and Composition of Functions Pg. 73# 121 – 123, 125 – 128 Pg. 67 # 9 – 17 odd, 39 – 42 all #1212L + 440#122l = 125, A = 125w #123t = 6.16 hrs#124r = 6.91 units #125P(n) = 0.50n – 18.25#126Graph #127D: {0,1,2…} R: {-18.25, -17.75, -17.25,…} #12837 tickets #1(∞,∞);(∞,∞);(∞,∞);(∞,0)U(0,∞) #3(∞,∞);(∞,∞);(∞,∞);(∞,0)U(0,∞) #5(∞,∞);(∞,∞);(∞,∞);(∞, ½)U(½,∞) #7D: (∞,4)U(4,∞) R: {-1,1} #9(f ◦ g)(3) = 8; (g ◦ f)(-2) = 3#11(f ◦ g)(3) = 9; (g ◦ f)(-2) = 66 #35Graph#36Graph#37Graph#38Graph

2. 1.6 Operations on Functions and Composition of Functions The perimeter P of a rectangle is given by the equation P = 2L + 2W, where L is the length and W is the width. If the width is 200 units, then write an equation for the perimeter P as a function of the length. Find a complete graph showing how P varies with length.

3. 1.6 Operations on Functions and Composition of Functions Composition of Functions Notation is given by: In order for a value of x to be in the domain of f◦g, two conditions must be met: – x must be in the domain of f – f(x) must be in the domain of g Practice Let and – Find and and determine their domain. Let and – Find and and determine their domain.

4. 1.6 Operations on Functions and Composition of Functions Composition of Functions Notation is given by: In order for a value of x to be in the domain of f◦g, two conditions must be met: – x must be in the domain of f – f(x) must be in the domain of g Practice Let f(x) = 2x + 1 and g(x) = x 1/2 - 2 – Find and and determine their domain. Let f(x) = 2x 3 - 1 and g(x) = x + 5 – Find and and determine their domain.

5. 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.

6. 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?