How is the composite function f0g defined? What is its domain?
> List the differences between chemical changes and physical changes.
> What is the function of oxaloacetate in the citric acid cycle?
> a. How many protons are in the nucleus of the isotope In-115? b. How many neutrons are in the nucleus of the isotope In-115?
> How many molecules of ATP are produced by the complete degradation of glucose via glycolysis, the citric acid cycle, and oxidative phosphorylation?
> An atom has nineteen protons, twenty neutrons, and nineteen electrons. Write the symbol of the atom.
> What products are formed when the v-phenyl-labeled carboxylic acid 5-phenylpentanoic acid is degraded by b-oxidation?
> Calculate the number of protons, neutrons, and electrons in: a. (17^37) Cl b. (11^23) Na c. (36^84) Kr
> Which reaction in b-oxidation is a hydration reaction? What is the name of the enzyme that catalyzes this reaction? Write an equation representing this reaction.
> What medical condition is indicated by elevated blood serum levels of amylase and lipase?
> The nuclei of three different atoms are depicted in the diagrams below. Which ones are isotopes, if any? = proton = neutron (a) (b) (c)
> What is the reactant that is oxidized in the reaction catalyzed by acyl-CoA dehydrogenase? What is the reactant that is reduced in this reaction?
> Label each of the following statements as true or false: a. An atom with an atomic number of 7 and a mass of 14 is identical to an atom with an atomic number of 6 and a mass of 14. b. Neutral atoms have the same number of electrons as protons. c. The mas
> The reaction catalyzed by fumarase is an example of the hydration of an alkene to produce an alcohol. Write the equation for this reaction. What is meant by the term hydration reaction?
> 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?
> (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 an explicit formula for f-1 and use it to graph f-1, f and the line y = x on the same screen. To check your work, see whether the graphs of f and f-1 are reflections about the line. f(x) = x* + 1, I> 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
