Problem 1E: Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of... Problem 2E: Explain how each graph is obtained from the graph ofy=f(x). (a) y=f(x)+8 (b) y=f(x+8) (c) y=8f(x)... Problem 3E: The graph of y=f(x) is given. Match each equation with its graph and give reasons for your choices.... Problem 4E: The graph of f is given. Draw the graphs of the following functions. (a) y=f(x)3 (b) y=f(x+1) (c)... Problem 5E: The graph of f is given. Use it to graph the following functions. (a) y=f(2x) (b) y=f(12x) (c)... Problem 6E: The graph of y=3xx2 is given. Use transformations to create a function whose graph is as shown. Problem 7E: The graph of y=3xx2 is given. Use transformations to create a function whose graph is as shown. Problem 8E Problem 9E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 10E Problem 11E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 12E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 13E Problem 14E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 15E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E: Graph the function by hand, not by plotting points, but by starting with the graph of one of the... Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E: The city of New Orleans is located at latitude 30N. Use Figure 9 to find a function that models the... Problem 28E: A variable star is one whose brightness alternately increases and decreases. For the most visible... Problem 29E Problem 30E: In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 500... Problem 31E: (a) How is the graph of y=f(|x|)related to the graph of f? (b) Sketch the graph of y=sin|x|. (c)... Problem 32E: Use the given graph of f to sketch the graph of y = 1/f(x). Which features of f are the most... Problem 33E: Find (a) f+g , (b) fg , (c) fg , and (d) f/g and state their domains. 33. f(x)=25x2,g(x)=x+1 Problem 34E: Find (a) f+g , (b) fg , (c) fg , and (d) f/g and state their domains. 34. f(x)=1x1,g(x)=1x2 Problem 35E: Find the functions (a) fg , (b) gf , (c) ff , and (d) gg and their domains. 35. f(x)=x3+5,g(x)=x3 Problem 36E: Find the functions (a) fg , (b) gf , (c) ff , and (d) gg and their domains. 36. f(x)=1x,g(x)=2x+1 Problem 37E Problem 38E: Find the functions (a) fg , (b) gf , (c) ff , and (d) gg and their domains. 38. f(x)=xx+1,g(x)=2x1 Problem 39E: Find the functions (a) fg , (b) gf , (c) ff , and (d) gg and their domains. 39. f(x)=2x,g(x)=sinx Problem 40E Problem 41E: Find f g h. 39. f(x) = 3x 2, g (x) = sin x, h(x) = x2 Problem 42E Problem 43E: Find f g h. 41.f(x)=x3, g(x) = x2, h(x) = x3 + 2 Problem 44E: Find f g h. 42. f(x) = tan x, g(x)=xx1,h(x)=x3 Problem 45E: Express the function in the form f g. 43. F(x) = (2x + x2)4 Problem 46E: Express the function in the form f g. 44. F(x) = cos2x Problem 47E Problem 48E Problem 49E: Express the function in the form f g. 47. v(t) = sec(t2) tan(t2) Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E: Use the table to evaluate each expression. 56. (a) g(g(g(2))) (b) (fff)(1) (c) (ffg)(1) (d) (gfg)(3) Problem 57E: Use the given graphs of f and g to evaluate each expression, or explain why it is undefined. (a)... Problem 58E: Use the given graphs of f and g to estimate the value of f(g(x)) for x = 5, 4, 3,. . . , 5. Use... Problem 59E: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60... Problem 60E: A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2... Problem 61E Problem 62E: An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a... Problem 63E: The Heaviside function H is defined by It is used in the study of electric circuits to represent the... Problem 64E Problem 65E: Let f and g be linear functions with equations f(x) = m1x + b1, and g(x) = m2x + b2. Is f g also a... Problem 66E Problem 67E: (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find a function f such that f g = h. (Think about... Problem 68E: If f(x) = x + 4 and h(x) = 4x 1, find a function g such that g f = h. Problem 69E: Suppose g is an even function and let h =f g. Is h always an even function? Problem 70E: Suppose g is an odd function and let h = f g. Is h always an odd function? What it f is odd? What... Problem 71E format_list_bulleted