Figure 1.41 shows f(t), the number (in millions) of motorvehicles registered19 in the

For the functions f in Exercises 13, graph: (a) f(x + 2) (b) f(x 1) (c) f(x) 4 (d) f(x + 1) + 3 (e) 3f(x) (f) f(x)+1 1

For the functions f in Exercises 13, graph: (a) f(x + 2) (b) f(x 1) (c) f(x) 4 (d) f(x + 1) + 3 (e) 3f(x) (f) f(x)+1 2

For the functions f in Exercises 13, graph: (a) f(x + 2) (b) f(x 1) (c) f(x) 4 (d) f(x + 1) + 3 (e) 3f(x) (f) f(x)+1 3

In Exercises 47, use Figure 1.37 to graph the functions. n(t) = m(t)+2

In Exercises 47, use Figure 1.37 to graph the functions. p(t) = m(t 1)

In Exercises 47, use Figure 1.37 to graph the functions. k(t) = m(t + 1.5)

In Exercises 47, use Figure 1.37 to graph the functions. w(t) = m(t 0.5) 2.5

For the functions f and g in Exercises 811, find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x) = x2, g(x) = x + 1

For the functions f and g in Exercises 811, find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x) = x + 4, g(x) = x2

For the functions f and g in Exercises 811, find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x) = ex, g(x) = x2

For the functions f and g in Exercises 811, find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x)=1/x, g(x)=3x + 4

For g(x) = x2 + 2x + 3, find and simplify: (a) g(2 + h) (b) g(2) (c) g(2 + h) g(2)

If f(x) = x2 + 1, find and simplify: (a) f(t + 1) (b) f(t 2 + 1) (c) f(2) (d) 2f(t) (e) (f(t))2 + 1

Simplify the quantities in Exercises 1417 using m(z) = z2. m(z + 1) m(z)

Simplify the quantities in Exercises 1417 using m(z) = z2. m(z + h) m(z)

Simplify the quantities in Exercises 1417 using m(z) = z2. m(z) m(z h)

Simplify the quantities in Exercises 1417 using m(z) = z2. m(z +h)m(zh)

Let p be the price of an item and q be the number of items sold at that price, where q = f(p). What do the following quantities mean in terms of prices and quantities sold? (a) f(25) (b) f1(30)

Let C = f(A) be the cost, in dollars, of building a store of area A square feet. In terms of cost and square feet, what do the following quantities represent? (a) f(10,000) (b) f1(20,000)

Let f(x) be the temperature (F) when the column of mercury in a particular thermometer is x inches long. What is the meaning of f1(75) in practical terms?

(a) Write an equation for a graph obtained by vertically stretching the graph of y = x2 by a factor of 2, followed by a vertical upward shift of 1 unit. Sketch it. (b) What is the equation if the order of the transformations (stretching and shifting) in part (a) is interchanged? (c) Are the two graphs the same? Explain the effect of reversing the order of transformations.

Use Figure 1.38 to graph each of the following. Label any intercepts or asymptotes that can be determined. (a) y = f(x)+3 (b) y = 2f(x) (c) y = f(x + 4) (d) y = 4 f(x)

For Exercises 2324, decide if the function y = f(x) is invertible. 23

For Exercises 2324, decide if the function y = f(x) is invertible. 24

For Exercises 2527, use a graph of the function to decide whether or not it is invertible. f(x) = x2 + 3x + 2

For Exercises 2527, use a graph of the function to decide whether or not it is invertible. f(x) = x3 5x + 10

For Exercises 2527, use a graph of the function to decide whether or not it is invertible. f(x) = x3 + 5x + 10

Are the functions in Exercises 2835 even, odd, or neither? f(x) = x6 + x3 + 1

Are the functions in Exercises 2835 even, odd, or neither? f(x) = x3 + x2 + x

Are the functions in Exercises 2835 even, odd, or neither? f(x) = x4 x2 + 3

Are the functions in Exercises 2835 even, odd, or neither? f(x) = x3 + 1

Are the functions in Exercises 2835 even, odd, or neither? f(x)=2x

Are the functions in Exercises 2835 even, odd, or neither? f(x) = ex21

Are the functions in Exercises 2835 even, odd, or neither? f(x) = x(x2 1)

Are the functions in Exercises 2835 even, odd, or neither? f(x) = ex x

For Problems 3639, determine functions f and g such that h(x) = f(g(x)). [Note: There is more than one correct answer. Do not choose f(x) = x or g(x) = x.] h(x)=(x + 1)3

For Problems 3639, determine functions f and g such that h(x) = f(g(x)). [Note: There is more than one correct answer. Do not choose f(x) = x or g(x) = x.] h(x) = x3 + 1

For Problems 3639, determine functions f and g such that h(x) = f(g(x)). [Note: There is more than one correct answer. Do not choose f(x) = x or g(x) = x.] h(x) = x2 + 4

For Problems 3639, determine functions f and g such that h(x) = f(g(x)). [Note: There is more than one correct answer. Do not choose f(x) = x or g(x) = x.] h(x) = e2x

Find possible formulas for the graphs in Problems 4041 using shifts of x2 or x3. 40

Find possible formulas for the graphs in Problems 4041 using shifts of x2 or x3. 41

(a) Use Figure 1.39 to estimate f1(2). (b) Sketch a graph of f1 on the same axes.

Write a table of values for f1, where f is as given below. The domain of f is the integers from 1 to 7. State the domain of f1.

For Problems 4447, decide if the function f is invertible f(d) is the total number of gallons of fuel an airplane has used by the end of d minutes of a particular flight.

For Problems 4447, decide if the function f is invertible f(t) is the number of customers in Macys department store at t minutes past noon on December 18, 2008.

For Problems 4447, decide if the function f is invertible f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.

For Problems 4447, decide if the function f is invertible f(w) is the cost of mailing a letter weighing w grams.

In Problems 4851 the functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The inflation begins at t = 0. In each case, give a mathematical expression that represents the given statement. The volume of the balloon t minutes after inflation began.

In Problems 4851 the functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The inflation begins at t = 0. In each case, give a mathematical expression that represents the given statement. The volume of the balloon if its radius were twice as big.

In Problems 4851 the functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The inflation begins at t = 0. In each case, give a mathematical expression that represents the given statement. The time that has elapsed when the radius of the balloon is 30 feet.

In Problems 4851 the functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The inflation begins at t = 0. In each case, give a mathematical expression that represents the given statement. The time that has elapsed when the volume of the balloon is 10,000 cubic feet.

In Problems 5255, use Figure 1.40 to estimate the function value or explain why it cannot be done. u(v(10))

In Problems 5255, use Figure 1.40 to estimate the function value or explain why it cannot be done. u(v(40))

In Problems 5255, use Figure 1.40 to estimate the function value or explain why it cannot be done. v(u(10))

In Problems 5255, use Figure 1.40 to estimate the function value or explain why it cannot be done. v(u(40))

Figure 1.41 shows f(t), the number (in millions) of motor vehicles registered19 in the world in the year t. (a) Is f invertible? Explain. (b) What is the meaning of f1(400) in practical terms? Evaluate f1(400). (c) Sketch the graph of f1.

For Problems 5762, use the graphs in Figure 1.42 Estimate f(g(1)).

For Problems 5762, use the graphs in Figure 1.42 Estimate g(f(2)).

For Problems 5762, use the graphs in Figure 1.42 Estimate f(f(1)).

For Problems 5762, use the graphs in Figure 1.42 Graph f(g(x)).

For Problems 5762, use the graphs in Figure 1.42 Graph g(f(x))

For Problems 5762, use the graphs in Figure 1.42 Graph f(f(x))

Figure 1.43 is a graph of the function f(t). Here f(t) is the depth in meters below the Atlantic Ocean floor where t million-year-old rock can be found.20 (a) Evaluate f(15), and say what it means in practical terms. (b) Is f invertible? Explain. (c) Evaluate f1(120), and say what it means in practical terms. (d) Sketch a graph of f1.

A tree of height y meters has, on average, B branches, where B = y1. Each branch has, on average, n leaves, where n = 2B2 B. Find the average number of leaves of a tree as a function of height.

A spherical balloon is growing with radius r = 3t + 1, in centimeters, for time t in seconds. Find the volume of the balloon at 3 seconds.

The cost of producing q articles is given by the function C = f(q) = 100 + 2q. (a) Find a formula for the inverse function. (b) Explain in practical terms what the inverse function tells you.

How does the graph of Q = S(1 ekt) in Example 4 on page 16 relate to the graph of the exponential decay function, y = Sekt?

Complete the following table with values for the functions f, g, and h, given that: (a) f is an even function. (b) g is an odd function. (c) h is the composition h(x) = g(f(x)).

In Problems 6971, explain what is wrong with the statement. The graph of f(x) = (x + 1)3 is the graph of g(x) = x3 shifted right by 1 unit.

In Problems 6971, explain what is wrong with the statement. f(x)=3x+5 and g(x) = 3x5 are inverse functions of each other.

In Problems 6971, explain what is wrong with the statement. The inverse of f(x) = x is f1(x)=1/x.

In Problems 7275, give an example of: An invertible function whose graph contains the point (0, 3).

In Problems 7275, give an example of: An even function whose graph does not contain the point (0, 0).

In Problems 7275, give an example of: An increasing function f(x) whose values are greater than those of its inverse function f1(x) for x > 0.

In Problems 7275, give an example of: Two functions f(x) and g(x) such that moving the graph of f to the left 2 units gives the graph of g and moving the graph of f up 3 also gives the graph of g.

Are the statements in Problems 7683 true or false? Give an explanation for your answer. The graph of f(x) = 100(10x) is a horizontal shift of the graph of g(x) = 10x.

Are the statements in Problems 7683 true or false? Give an explanation for your answer. If f is an increasing function, then f1 is an increasing function.

Are the statements in Problems 7683 true or false? Give an explanation for your answer. If a function is even, then it does not have an inverse

Are the statements in Problems 7683 true or false? Give an explanation for your answer. If a function is odd, then it does not have an inverse.

Are the statements in Problems 7683 true or false? Give an explanation for your answer. The function f(x) = ex2 is decreasing for all x

Are the statements in Problems 7683 true or false? Give an explanation for your answer. . If g(x) is an even function then f(g(x)) is even for every function f(x).

Are the statements in Problems 7683 true or false? Give an explanation for your answer. If f(x) is an even function then f(g(x))is even for every function g(x).

Are the statements in Problems 7683 true or false? Give an explanation for your answer. There is a function which is both even and odd.

Suppose f is an increasing function and g is a decreasing function. In Problems 8487, give an example for f and g for which the statement is true, or say why such an example is impossible. f(x) + g(x) is decreasing for all x.

Suppose f is an increasing function and g is a decreasing function. In Problems 8487, give an example for f and g for which the statement is true, or say why such an example is impossible. f(x) g(x) is decreasing for all x

Suppose f is an increasing function and g is a decreasing function. In Problems 8487, give an example for f and g for which the statement is true, or say why such an example is impossible. f(x)g(x) is decreasing for all x.

Suppose f is an increasing function and g is a decreasing function. In Problems 8487, give an example for f and g for which the statement is true, or say why such an example is impossible. f(g(x)) is increasing for all x.