Question: Find an explicit formula for f-1

> Why is the number of electrons not part of the mass number of an atom?

> Which bond in fatty acyl CoA is a high-energy bond?

> Using periodic trends, rank Br, I, and F in order of increasing a. atomic size b. ionization energy c. electron affinity

> The pair of reactions catalyzed by aconitase results in the conversion of isocitrate to its isomer citrate. What are isomers?

> Discuss the difference between theory and scientific law.

> What is the function of colipase in the digestion of dietary lipids?

> Describe the process occurring at the molecular level that accounts for the property of surface tension.

> The model of methane in Question 1.27 has limitations, as do all models. What are these limitations? Question 1.27: What are the characteristics of methane emphasized by the following model? H H°c H H

> a. What are very low-density lipoproteins? b. Compare the function of VLDLs with that of chylomicrons.

> What data would be required to estimate the mass of planet earth?

> Why are triglycerides more efficient energy-storage molecules than glycogen?

> Why is observation a critical starting point for any scientific study?

> Why are the lipases that are found in saliva and in the stomach not very effective at digesting triglycerides?

> Define energy and explain the importance of energy in chemistry.

> What is the major metabolic function of adipose tissue?

> Convert 2.00 × 102 J to units of cal.

> What tissue is the major storage depot for lipids?

> How does the reaction described in Question 22.101 allow the citric acid cycle to fulfill its roles in both catabolism and anabolism? Question 22.101: Write a balanced equation for the reaction catalyzed by pyruvate carboxylase.

> Report the result of each of the following operations using the proper number of significant figures: 27.2 x 15.63 а. 4.79 x 105 с. 3.58 е. 4.0 1.84 0.7911 11.4 x 10-4 f. 13.6 b. 18.02 x 1.6 d. 3.58 x 4.0 = 0.45

> Why is colipase needed for lipid digestion?

> Report the result of the following addition to the proper number of significant figures and in scientific notation. 4.80 × 108 + 9.149 × 102

> Draw the structure of a triglyceride composed of glycerol, palmitoleic acid, linolenic acid, and oleic acid.

> Report the result of each of the following to the proper number of significant figures: a. 7.939 + 6.26 = b. 2.4 - 8.321 = c. 2.333 + 1.56 - 0.29 =

> In Figure 23.1, a micelle composed of the phospholipid lecithin is shown. Why is lecithin a good molecule for the formation of micelles? Figure 23.1: H,C-0-C-R,. HC-0-C-R2 НС — О— Р-О -0 CH2 CH2 CH, +N4 -CH3 CH3

> Using the periodic table, write the symbol for each of the following and label as a metal, metalloid, or nonmetal. a. sulfur b. oxygen c. phosphorus d. nitrogen

> To what class of lipids do the bile salts belong?

> Represent each of the following numbers in scientific notation, showing only significant digits: a. 48.20 b. 480.0 c. 0.126 d. 9,200 e. 0.0520 f. 822

> Summarize the effects of the hormone glucagon on carbohydrate and lipid metabolism.

> Draw the Lewis structure of each of the following compounds and predict its geometry using the VSEPR theory. a. SeO2 b. SeO3

> Predict which of the following bonds are polar, and, if polar, use a vector to indicate in which direction the electrons are pulled: a. Si—Cl b. S—Cl c. H—C d. C—C

> List five biological activities that require ATP.

> Use transformations to sketch the graph of the function. y = -sin 2x

> Draw, by hand, a rough sketch of the graph of each function. (a). y = sin x (b). y = tan x (c). y = ex (d). y = ln x (e). y = 1/x (f). y = |x| (g). y = √x

> Sketch by hand, on the same axes, the graphs of the following functions. (a). f (x) = x (b). g (x) = x2 (c). h (x) = x3 (d). j (x) = x4

> What is a mathematical model?

> What is an increasing function?

> How is the composite function f0g defined? What is its domain?

> (a). Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b). Eliminate the parameter to find a Cartesian equation of the curve. х 3 3t — 5, у 3D 2t + 1

> Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as increases. x = t? + 1, y = t² - t, -2 <t< 2

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. f (x) = x2 - 2x

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. y

> (a). What is a parametric curve? (b). How do you sketch a parametric curve? (c). Why might a parametric curve be more useful than a curve of the form y = f (x)?

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. у.

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. yA

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. 1 2 3 4 5 6 f(x) 1.0 1.9 2.8 3.5 3.1 2.9

> Find the exact value of each expression. (a). log2 6 - log2 15 + log2 20 (b). log3 100 - log3 18 - log3 50

> Let g (x) = 3√1-x3. (a). Find g-1. How is it related to g? (b). Graph g. How do you explain your answer to part (a)?

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. 1 2 3 4 5 6 f(x) 1.5 2.0 3.6 5.3 2.8 2.0

> Find a formula for the inverse of the function. f (x) = 1 + √2 + 3x

> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. If f is a function, then f (s + t) = f (s) + f (t). 2. If f (s) = f (t), then s = t. 3. If f is

> (a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = tan*e, y = sec 0, -7/2 < 0 < m/2

> (a). If f0 (x) = 1/ 2-x and fn+1 = f00 fn for n = 0, 1, 2, find an expression for fn (x) and use mathematical induction to prove it. (b). Graph f0, f1, f2, f3 on the same screen and describe the effects of repeated composition.

> Prove that 1 + 3 + 5 + … + (2n -1) = n2.

> Prove that if n is a positive integer, then 7n -1 is divisible by 6.

> Is it true that f 0 (g+ h) = f0g + f0h?

> A driver sets out on a journey. For the first half of the distance she drives at the leisurely pace of 30 mi/h; she drives the second half at 60 mi/h. What is her average speed on this trip?

> Use indirect reasoning to prove that log25 is an irrational number.

> Sketch the region in the plane consisting of all points (x, y) such that |x – y| + |x| - |y| < 2

> Sketch the region in the plane consisting of all points (x, y) such that |x| + |y| < 1.

> Draw the graph of the equation x + |x| = y + |y|.

> Solve the inequality |x – 1| - |x - 3| > 5.

> Suppose the graph of f is given. Write an equation for each of the graphs that are obtained from the graph of f as follows. (a). Shift 2 units upward. (b). Shift 2 units downward. (c). Shift 2 units to the right. (d). Shift 2 units to the left. (e). Refl

> Solve the equation |2x – 1| - |x – 5| = 3.

> (a). Find parametric equations for the set of all points P determined as shown in the figure such that |OP| = |AB|. (This curve is called the cissoid of Diocles after the Greek scholar Diocles, who introduced the cissoid as a graphical method for constru

> (a). Find parametric equations for the path of a particle that moves counterclockwise halfway around the circle (x – 2)2 + y2 = 4, from the top to the bottom. (b). Use the equations from part (a) to graph the semicircular path.

> Graph members of the family of functions f (x) = ln (x2 -c) for several values of c. How does the graph change when changes?

> A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and $12,000 to produce 1500 toaster ovens a week. (a). Express the cost as a function of the number of toaster ovens produced, assuming that it is linear. Then

> Life expectancy improved dramatically in the 20th century. The table gives the life expectancy at birth (in years) of males born in the United States. Use a scatter plot to choose an appropriate type of model. Use your model to predict the life span of a

> Find an expression for the function whose graph consists of the line segment from the point (-2, 2) to the point (-1, 0) together with the top half of the circle with center the origin and radius 1.

> Determine whether is even, odd, or neither even nor odd. (a). f (x) = 2x5 – 3x2 + 2 (b). f (x) = x3 – x7 (c). f (x) = e-x2 (d). f (x) = 1 + sin x

> The graph of f is given. Draw the graphs of the following functions. 1 (а) у — /(x — 8) (c) у — 2 — f(u) (e) y =f-(x) (b) у — —f(x) (d) у — /) — 1 (f) y = f-(x + 3)

> Suppose that the graph of f is given. Describe how the graphs of the following functions can be obtained from the graph of f. (а) у — f() + 8 (с) у — 1 + 2f(х) (е) у — —f(») (b) у —f(x + 8) (d) у — f(x — 2) — 2 (f) y =f-(x)

> (a). What is an even function? How can you tell if a function is even by looking at its graph? (b). What is an odd function? How can you tell if a function is odd by looking at its graph?

> The graph of is given. (a). State the value of g (2). (b). Why is one-to-one? (c). Estimate the value of g-1 (2). (d). Estimate the domain of g-1. (e). Sketch the graph of g-1. 0 1

> (a). If we shift a curve to the left, what happens to its reflection about the line y = x? In view of this geometric principle, find an expression for the inverse of g (x) = f (x + c), where f is a one-to-one function. (b). Find an expression for the inv

> Starting with the graph of y = ln x, find the equation of the graph that results from (a). shifting 3 units upward (b). shifting 3 units to the left (c). reflecting about the x-axis (d). reflecting about the y-axis (e). reflecting about the line y = x (f

> Let f be the function whose graph is given. f (a). Estimate the value of f (2). (b). Estimate the values of such that f (x) = 3. (c). State the domain of f. (d). State the range of f. (e). On what interval is f increasing? (f). Is f one-to-one? Explain

> (a). What is a one-to-one function? How can you tell if a function is one-to-one by looking at its graph? (b). If f is a one-to-one function, how is its inverse function defined? How do you obtain the graph of f-1 from the graph of f?

> (a). If g (x) = x6 + x4, x > 0 use a computer algebra system to find an expression for g-1 (x). (b). Use the expression in part (a) to graph y = g (x), y = x, and y = g-1 (x) on the same screen.

> Graph the function f (x) = √x3 + x2 + x + 1 and explain why it is one-to-one. Then use a computer algebra system to find an explicit expression for f-1(x). (Your CAS will produce three possible expressions. Explain why two of them are irrelevant in this

> Suppose that f has domain A and g has domain B. (a). What is the domain of f + g? (b). What is the domain of fg? (c). What is the domain of f/g?

> Starting with the graph of y = ex, find the equation of the graph that results from (a) reflecting about the line y = 4 (b) reflecting about the line x = 2

> Compare the functions f (x) = x0.1 and g (x) = in x by graphing both f and g in several viewing rectangles. When does the graph of f finally surpass the graph of g?

> Graph the given functions on a common screen. How are these graphs related? у 3 3, у— 10+, у-()', у— (Э)"

> Use Formula 10 to graph the given functions on a common screen. How are these graphs related? y = ln x, y = log10 x, y = ex, y = 10x

> Use Formula 10 to graph the given functions on a common screen. How are these graphs related? y = log1.5 x, y = ln x, y = log10 x, y = log50 x

> Graph several members of the family of functions f (x) = 1 /1 + aebx where a > 0. How does the graph change when changes? How does it change when a change?

> Let f(x) = √1-x2, o < x < 1 (a). Find f-1. How is it related to f? (b). Identify the graph of f and explain your answer to part (a).

> A bacterial culture starts with 500 bacteria and doubles in size every half hour. (a). How many bacteria are there after 3 hours? (b). How many bacteria are there after t hours? (c). How many bacteria are there after 40 minutes? (d). Graph the population

> Make a rough sketch of the graph of each function. Do not use a calculator. Just use the graphs given in Figures 12 and 13 and, if necessary, the transformations of Section 1.3. Figures 12: Figures 13: (a). y = ln (-x) (b). y = ln |x| y y= log,

> Make a rough sketch of the graph of each function. Do not use a calculator. Just use the graphs given in Figures 12 and 13 and, if necessary, the transformations of Section 1.3. Figures 12: Figures 13: (a). y = log10(x + 5) (b). y = -ln x y y=

> Investigate the family of curves defined by the parametric equations x = cos t, y = sin t – sin ct, where c > 0. Start by letting be a positive integer and see what happens to the shape as c increases. Then explore some of the possibilities that occur wh

> The curves with equations x = a sin nt, y = b cos t is called Lissajous figures. Investigate how these curves vary when a, b, and n vary. (Take n to be a positive integer.)

> The swallowtail catastrophe curves are defined by the parametric equations x = 2ct - 4t3, y = -ct2 + 3t4. Graph several of these curves. What features do the curves have in common? How do they change when c increases?

> Graph the given functions on a common screen. How are these graphs related? у %3е*, у—е", у38%, у- 8*

> Investigate the family of curves defined by the parametric equations x = t2, y = t3 - ct. How does the shape change c as increases? Illustrate by graphing several members of the family.

> If a projectile is fired with an initial velocity of meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position after seconds is given by the parametric equations where is the acceleration due

> Suppose that the position of one particle at time is given by x1 = 3 sin t y1 = 2 cos t 0 (a). Graph the paths of both particles. How many points of intersection are there? (b). Are any of these points of intersection collision points? In other words,

> A curve, called a witch of Maria Agnesi, consists of all possible positions of the point P in the figure. Show that parametric equations for this curve can be written as Sketch the curve. x = 2a cot e y = 2a sin?e y у. C y = 2a --- at