Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1 – 1/x
> A ship is moving at a speed of 30 km/h parallel to a straight shoreline. The ship is 6 km from shore and it passes a lighthouse at noon. a. Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled
> A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s. a. Express the radius r of the balloon as a function of the time t (in seconds). b. If V is the volume of the balloon as a function of the radius, fi
> A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. a. Express the radius r of this circle as a function of the time t (in seconds). b. If A is the area of this circle as a function of the radius, find
> Use the given graphs of f and g to estimate the value of f(g(x)) for x = 25, 24, 23,..., 5. Use these estimates to sketch a rough graph of f 0 g. 1 f
> Use the given graphs of f and g to evaluate each expression, or explain why it is undefined. a. f(g(2)) b. g(f(0)) c. (f 0 g)(0) d. (g 0 f)(6) e. (g 0 g)(-2) f. (f 0 f)(4) 19 f 2 2.
> Use the table to evaluate each expression. a. f(g(1)) b. g(f(1)) c. f(f(1)) d. g(g(1)) e. (g 0 f)(3) f. (f 0 g)(6) 1 3 4 5 f(x) 3 1 4 2 2 5 g(x) 3 2 1 2 3
> Sketch a rough graph of the number of hours of daylight as a function of the time of year.
> Express the function in the form f 0 g 0 h. S(t) = sin2(cos t)
> Express the function in the form f 0 g 0 h. H(x) = 8 2 +|x|
> Express the function in the form f 0 g 0 h. R(x) =√ x − 1
> Express the function in the form f 0 g. u(t) =tan t / 1 + tan t
> Express the function in the form f 0 g. v(t) = sec(t2) tan(t2)
> Express the function in the form f 0 g. G(x) = 3 x/ 1+x
> Express the function in the form f 0 g. F(x) = ∛x / 1 + ∛x
> Express the function in the form f 0 g. F(x) = cos2x
> Express the function in the form f 0 g. F(x) = (2x + x2)4
> Find f 0 g 0 h. f(x) = tan x, g(x) = x/x - 1, h(x) = 3√ x
> The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; t is measured in hours starting at midnight.) a. What was the power consumption at 6 am? At 6 pm? b. When was the power consumption the lowest?
> Find f 0 g 0 h. f(x) =
> Find f 0 g 0 h. f(x) =|x - 4|, g(x) = 2x, h(x) = √x
> Find f 0 g 0 h. f(x) = 3x - 2
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. F(x) = x / 1 + x , g(x) = sin 2x
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. f(x) = x + 1 / x , g(x) = x + 1 / x + 2
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. f(x) = sin x, g(x) = x2 + 1
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. f(x) = x + 1 , g(x) = 4x - 3
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. f(x) = x3 - 2, g(x) = 1 - 4x
> Find the functions a. f 0 g, b. g 0 f, c. f 0 f, and d. g 0 g and their domains. f(x) = 3x + 5, g(x) = x2 + x
> Find a. f + t, b. f - t, c. ft, and d. f/t and state their domains. f(x) = 3 − x , g(x) = x2 − 1
> Three runners compete in a 100-meter race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who won the race? Did each runner finish the race? y4 (meters) AB C 100
> Find a. f + t, b. f - t, c. ft, and d. f/t and state their domains. f(x) = x3 + 2x2, g(x) = 3x2 - 1
> Use the given graph off to sketch the graph of y = 1/f(x). Which features of f are the most important in sketching y = 1/f(x)? Explain how they are used. yA 1
> a. How is the graph of y = f(|x|) related to the graph off ? b. Sketch the graph of y = sin|x|. c. Sketch the graph of y = √|x|.
> In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 500 mL. The reserve and residue volumes of air that remain in the lungs occupy about 2000 mL and a single respiratory cycle for an average human takes about 4 s
> Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is about 12 hours and on
> A variable star is one whose brightness alternately increases and decreases. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average brightness (or magnitude) of the star is 4.0, and its b
> The city of New Orleans is located at latitude 30°N. Use Figure 9 to find a function that models the number of hours of daylight at New Orleans as a function of the time of year. To check the accuracy of your model, use the fact that on March
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y =| cosπ x|
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y =|√x - 1|
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = ¼ tan (x – π/4)
> You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Describe how the temperature of the water changes as time passes. Then sketch a rough graph of the temperature of the water as a function of the ela
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = |x - 2|
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y =|x|- 2
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = sin(1/2x)
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 3 - 2 cos x
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 2 - √x
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1 + sinπ x
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = x2 - 4x + 5
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 2 x + 1
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 2 cos 3x
> Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in cooler years. The figure shows ring widths of a Siberian pine from 1500 to 2000. a. What is the range of the ring width function? b. What does the grap
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = x3 + 1
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = (x - 3)2
> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = -x2
> a. How is the graph of y = 2sinx related to the graph of y = sinx? Use your answer and Figure 6 to sketch the graph of y = 2sinx. b. How is the graph of y = 1 + √x related to the graph of y = √x ? Use your answer and
> The graph of y = 3x − x2 is given. Use transformations to create a function whose graph is as shown. yA 1.5- y=V3x– x² 3 yA -4 -1 0 --2.5
> The graph of y = 3x − x2 is given. Use transformations to create a function whose graph is as shown. yA 1.5- y=V3x– x² 3 y. 3- 5 х 2.
> The graph off is given. Use it to graph the following functions. a. y = f(2x) b. y = f(1/2x) c. y = f(-x) d. y = 2f(-x) yA 1 이 1
> Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.) a.y=3x b. y = 3x c. y = x3 d. y = 3
> Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.) a. y = x2 b. y = x5 c. y = x8 4.
> Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. a. y = πx b. y = x π c. y = x2(2 - x3) d. y = tan t
> Shown is a graph of the global average temperature T during the 20th century. Estimate the following. a. The global average temperature in 1950 b. The year when the average temperature was 14.2°C c. The year when the temperature was smalles
> Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. a. f(x) = log2 x b. g(x) = 4
> The table shows the mean (average) distances d of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods T (time of revolution in years). a. Fit a power model to the data. b. Kepler&acir
> The table shows the number N of species of reptiles and amphibians inhabiting Caribbean islands and the area A of the island in square miles. a. Use a power function to model N as a function of A. b. The Caribbean island of Dominica has area 291 mi2. H
> It makes sense that the larger the area of a region, the larger the number of species that inhabit the region. Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in cave
> Many physical quantities are connected by inverse square laws, that is, by power functions of the form f(x) = kx-2. In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Su
> The table shows average US retail residential prices of electricity from 2000 to 2012, measured in cents per kilowatt hour. a. Make a scatter plot. Is a linear model appropriate? b. Find and graph the regression line. c. Use your linear model from par
> The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day. a. Make a scatter plot and decide whether a linear model is appropriate. b. Find and graph the regression line. c. Use the linear model to
> When laboratory rats are exposed to asbestos fibers, some of them develop lung tumors. The table lists the results of several experiments by different scientists. a. Find the regression line for the data. b. Make a scatter plot and graph the regression
> Anthropologists use a linear model that relates human femur (thighbone) length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. Here we find the model by a
> Biologists have observed that the chirping rate of crickets of a certain species appears to be related to temperature. The table shows the chirping rates for various temperatures. a. Make a scatter plot of the data. b. Find and graph the regression lin
> Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function. 이 1
> If f(x) = x + 2−
> What three data anomalies are likely to be the result of data redundancy? How can such anomalies be eliminated?
> What is normalization?
> Is it possible for a book to appear in the BOOK table without appearing in the PRODUCT table? Why or why not?
> According to the data model, is it required that every entity instance in the PRODUCT table be associated with an entity instance in the CD table? Why or why not?
> List all of the attributes of a movie.
> What is the difference between partial completeness and total completeness?
> What is an overlapping subtype? Give an example.
> What is a subtype discriminator? Given an example of its use.
> What is a specialization hierarchy?
> What kinds of data would you store in an entity subtype?
> Why may the client/server evolution be characterized as a bottom-up change and how does this change affect the computing environment?
> What is the most common design trap, and how does it occur?
> Using an ER diagram, illustrate how the change you made in problem 1 affects the relationship of the USER entity to the following entities: LAB_USE_LOG RESERVATION CHECK_OUT WITHDRAW
> Verify the conceptual model you created in Appendix B, problem 3. Create a data dictionary for the verified model.
> Tiny College wants to keep track of the history of all administrative appointments (date of appointment and date of termination). (Hint: Time variant data are at work.) The Tiny College chancellor may want to know how many deans worked in the College of
> Research – and document -- the purchase of a new house. Requirements: a. What web sites did you visit? b. Classify each site (B2B, B2C, and so on.) c. What information did you collect? Was the information useful? Why or why not? d. What decision(s) did y
> Research – and document -- the purchase of a new car. Based on your research, explain why you plan to buy this car. Requirements: a. What web sites did you visit? b. Classify each site (B2B, B2C, and so on.) c. What information did you collect? Was the i
> Use the Internet at your university computer lab or home to research the scenarios described in Problems 1-10. Then work through the following problems: a. What web sites did you visit? b. Classify each site (B2B, B2C, and so on.) c. What information did
> Using the contracting company’s ERD in Chapter 6, “Normalization of Database Tables,” Figure 6.15, create the equivalent OO representation.
> Using the ERD shown in Appendix C, “The University Lab Conceptual Design Verification, Logical Design, and Implementation,” Figure C.22 (the Check_Out component), create the equivalent OO representation.
> Convert the following relational database tables to the equivalent OO conceptual representation. Explain each of your conversions with the help of a diagram. ) Note: The Avion Sales database includes the tables shown in Figure PG.7). FIGURE PG.7 TheAvio
> Why may client/server computing be considered an evolutionary, rather than a revolutionary, change?
> Convert the following relational database tables to the equivalent OO conceptual representation. Explain each of your conversions with the help of a diagram. (Note: The R&C Stores database includes the three tables shown in Figure PG.6) FIGURE PG.6
> Assume the following business rules: • A course contains many Sections, but each Section references only one course. • A Section is taught by one professor, but each professor may teach one or more different Sections of one or more courses. • A Section m
> Given the information in Problem 1, define a superclass VEHICLE for the TRUCK class. Redraw the object space you developed in Problem 3, taking into consideration the new superclass that you just added to the class hierarchy.
> Using the data presented in Problem 1, develop an object space diagram representing the object's state for the instances of TRUCK listed below. Label each component clearly with proper OIDs and attribute names. a. The instance of the class TRUCK with TRU
> Using the tables in Figure PG.1 as a source of information: a. Define the implied business rules for the relationships. b. Using your best judgment, choose the type of participation of the entities in the relationship (mandatory or optional). Explain you
