Problem 1QC: If f(x)=x22x, find f(1),f(x2),f(t), and f(p1). Problem 2QC: State the domain and range of f(x)=(x2+1)1. Problem 3QC: If f(x)=x2+1 and g(x)=x2, find fg and gf. Problem 4QC: Refer to Figure 1.12. Find the hiker's average speed during the first mile of the trail and then... Problem 5QC: Explain why the graph of a nonzero function is never symmetric with respect to the x-axis. Problem 1E: Use the terms domain, range, independent variable, and dependent variable to explain how a function... Problem 2E: Is the independent variable of a function associated with the domain or range? Is the dependent... Problem 3E: Vertical line test Decide whether graphs A, B, or both represent functions. 11. Problem 4E: The entire graph of f is given. State the domain and range of f. Problem 5E: Which statement about a function is true? (i) For each value of x in the domain, there corresponds... Problem 6E Problem 7E: Determine the domain and range of f(x)=3x210. Problem 8E: Domain in context Determine an appropriate domain of each function. Identify the independent and... Problem 9E: Domain in context Determine an appropriate domain of each function. Identify the independent and... Problem 10E: If f(x) = 1/(x3 + 1), what is f(2)? What is f(y2)? Problem 11E: Let f(x)=2x+1 and g(x)=1/(x1). Simplify the expressions f(g(1/2)),g(f(4)), and g(f(x)). Problem 12E: Find functions f and g such that f(g(x))=(x2+1)5. Find a different pair of functions and g that also... Problem 13E: Explain how to find the domain of fg if you know the domain and rnge of f and g. Problem 14E: If f(x)=x and g(x)=x32, simplify the expressions (fg)(3),(ff)(64),(gf)(x), and (fg)(x). Problem 15E: Composite functions from graphs Use the graphs of f and g in the figure to determine the following... Problem 16E: Composite functions from tables Use the table to evaluate the given compositions. a. h(g(0)) b.... Problem 17E: Rising radiosonde The National Weather Service releases approximately 70,000 radiosondes every year... Problem 18E: World record free fall On October 14, 2012, Felix Baumgartner stepped off a balloon capsule at an... Problem 19E: Suppose f is an even function with f(2) = 2 and g is an odd function with g(2) = 2. Evaluate f(2),... Problem 20E: Complete the left half of the graph of g if g is an odd function. Problem 21E Problem 22E Problem 23E: Domain and range State the domain and range of the function. 23.f(x)=x25x+6x2 Problem 24E: Domain and range State the domain and range of the function. 24.f(x)=x22x Problem 25E: Domain and range State the domain and range of the function. 25.f(x)=7x2 Problem 26E: Domain and range State the domain and range of the function. 26.f(x)=25x2 Problem 27E: Domain State the domain of the function. 27.h(u)=u13 Problem 28E: Domain State the domain of the function. 28.F(w)=2w4 Problem 29E: Domain State the domain of the function. 29.f(x)=(9x2)3/2 Problem 30E: Domain State the domain of the function. 30.g(t)=11+t2 Problem 31E: Launching a rocket A small rocket is launched vertically upward from the edge of a cliff 80 ft off... Problem 32E: Draining a tank (Torricellis law) A cylindrical tank with a cross-sectional area of 10 m2 is filled... Problem 33E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 34E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 35E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 36E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 37E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 38E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 39E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 40E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 41E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 42E: Composite functions and notation Let f(x) = x2 4, g(x) = x3, and F(x) = l/(x 3). Simplify or... Problem 43E: Working with composite functions Find possible choices for outer and inner functions f and g such... Problem 44E: Working with composite functions Find possible choices for outer and inner functions f and g such... Problem 45E: Working with composite functions Find possible choices for outer and inner functions f and g such... Problem 46E: Working with composite functions Find possible choices for outer and inner functions f and g such... Problem 47E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the... Problem 48E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the... Problem 49E Problem 50E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the... Problem 51E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the... Problem 52E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x)=1/(x2). Determine the... Problem 53E Problem 54E: More composite functions Let f(x) = |x|, g(x) = x2 4, F(x)=x, and G(x) = 1/(x 2). Determine the... Problem 55E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 49. (f ... Problem 56E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 50.... Problem 57E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 51. (f ... Problem 58E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 52. (f ... Problem 59E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 53. (g ... Problem 60E: Missing piece Let g(x) = x2 + 3. Find a function f that produces the given composition. 54. (g ... Problem 61E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 62E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 63E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 64E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 65E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 66E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 67E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 68E: Working with difference quotients Simplify the difference quotient f(x+h)f(x)h for the following... Problem 69E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 70E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 71E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 72E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 73E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 74E: Working with difference quotients Simplify the difference quotient f(x)f(a)xa for the following... Problem 75E: GPS data A GPS device tracks the elevation E (in feet) of a hiker walking in the mountains. The... Problem 76E: Elevation vs. Distance The following graph, obtained from GPS data, shows the elevation of a hiker... Problem 77E: Interpreting the slope of secant lines In each exercise, a function and an interval of its... Problem 78E: Interpreting the slope of secant lines In each exercise, a function and an interval of its... Problem 79E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 80E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 81E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 82E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 83E Problem 84E Problem 85E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 86E: Symmetry Determine whether the graphs of the following equations and functions are symmetric about... Problem 87E: Composition of even and odd functions from graphs Assume f is an even function and g is an odd... Problem 88E: Composition of even and odd functions from tables Assume f is an even function and g is an odd... Problem 89E: Absolute value graph Use the definition of absolute value to graph the equation |x| |y| = 1. Use a... Problem 90E: Graphing semicircles Show that the graph of f(x)=10+x2+10x9 is the upper half of a circle. Then... Problem 91E: Graphing semicircles Show that the graph of g(x)=2x2+6x+16 is the lower half of a circle. Then... Problem 92E: Even and odd at the origin a. If f(0) is defined and f is an even function, is it necessarily true... Problem 93E: Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:... Problem 94E: Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:... Problem 95E: Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:... Problem 96E: Polynomial calculations Find a polynomial f that satisfies the following properties. (Hint:... Problem 97E: Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing... Problem 98E: Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing... Problem 99E: Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing... Problem 100E: Difference quotients Simplify the difference quotients f(x+h)f(x)h and f(x)f(a)xa by rationalizing... Problem 101E Problem 102E Problem 103E Problem 104E format_list_bulleted