H.W. for MAC 1147H
The following lists the problems that you should be able to do on your own. Some of these problems will be formally
assigned to be turned in and graded. I will also be adding problems to the list as the semester goes along.
The page number refers to the .pdf page number using acrobat.
The symbol * is used to indicate that this is a harder problem.
By Chapters:
Chapter 1.1, P. 19-21
Definition of a function, vertical line test, one-to-one and horizontal line test,
indeterminants/variables, inputs (independent variable) and outputs (dependent variable)
8-14, 16-19, 20*, 21, 22,27-31, 32*, 33*, 35, 37, 40-51, 53-67 odd, 91.
Chapter 1.2, P. 35-37
domain and range: interval notation and other notations, polynomials, linear and quadratics, radicals
roots and denominators, piecewise polynomial, absolute value,
3, 7-25 odd, 26a.*, 27-37 odd, 47-53 odd, 57*, 60*, 61.
Chapter 1.3, P. 48-50
average rate of change of interval [a,b], Delta notation, increasing, decreasing, local max and min, absolute max and min,
3, 5-15 odd, 17, 18, 22, 23, 24, 25, 29-31 odd, 42*, 43*, 44, 46, 47.
Chapter 1.4, P. 60-63
sum/difference, ratios, products, composition, domain of composition, composition is not commutative
3, 5-21 odd, 27, 35, 39, 43-49 odd, 54-57, 59, 63, 73, 75, 77, 79, 80, 81, 83, 85, 86, 93*, 96*, 97.
typo Figure 7 should be labelled g(x)
Chapter 1.5, P. 85-88
vertical and horizontal shifts, reflections about x-axis and y-axis, even odd, neither, combine transformations,
11-19, 21, 23, 33-41 odd, 47-61 odd.
Chapter 1.6, P. 98-99
absolute value functions
6, 7, 9, 11-23 odd, 25-35 odd, 39, 41-51 odd, 57*, 59*, 61*
Chapter 1.7, P. 110-112
inverse functions
3, 13, 15, 17, 23, 25-32, 33-41 odd, 47
Chapter 2.1, P. 139-142
linear functions, point-slope form, slope-intercept form
3, 5, 6, 7-39 odd, 40, 41, 43, 45, 47, 63*, 65*, 66*, 67*, 69, 76
Chapter 2.2, P. 159-161
system of two equations and two unknowns, parallel or perpendicular or neither, x-intercepts, y-intercepts
7-27 odd, 31, 32-37, 39, 45-57 odd, 59, 61, 64, 65-69 odd,
Chapter 3.2, P. 221-223
quadratic equations, parabola, vertex, general form, completing the square, standard form: a(x-h)^2+k,
axis of symmetry, quadratic formula, h=-b/2a, k=f(h)
7-25 odd, 45, 47, 53, 55, 59, 60, 61, 85-92,
Chapter 3.3, P. 236-238
polynomials, power function, generalized polynomials, rational functions, graphs, end behavior,
degree, leading coeffecient, constant term, general form of a polynomail,
7-37 odd, 39-45 (which could be graphs of a polynomial?)
Chapter 3.4, P. 254-256
domain of polynomials, find x-intercepts by factoring, find y-intercepts,
x-intercept is also called a zero of the function or root of the function, mutliplicity of a root,
maximum number of turning points, IVT,
7-21 odd, 25, 27, 29, 31-41 odd, 75, 77, 79
**- will be skipping on constructing a polynomial whose graph is the given graph.
Chapter 3.5, P. 264-265
division algorithm for the integers, division algorithm for polynomials,
the point is to use division to factor, dividend = divisor times quotient + remainder,
will only discuss synthetic division but will not cover it
3-13 odd, 45, 47, 65, 67
Chapter 3.7, P. 295-298
rational functions, vertical asymptotes, domain of function, removable discontinuities, horizontal asymptote,
slant asymptotes, graphing rational functions
6-9, 11-29 odd, 39-45 odd, 49, 75-79, 81* -- removed 31, 33, 47 slant asymptote
Chapter 3.8, P.
5*, 7*, 9*, 11*, 13, 15, 17-27 odd, 29*, 31*, 57, 59, 63, 53, 55
42-46: just find domain
Chapter 4.1, P. 340-342
expoenential growth and decay, exponential functions, f(x)=abx, base b has to be positive and not 1,
finding equations of exponential functions, compond interest A(t)=P(1+ r/n)nt, base e=\lim (1+1/n)n.
4-7, 9-12 use calculator, 14-17, 31, 33, 34, 35, 36*, 39, 41, 45-49 odd, 61-67 odd
Chapter 4.2, P. 352-354
transformations of exponential, vertical and horizontal shifts,
13-22, 29-37 odd, 39, 41
Chapter 4.3, P. 361-362
logarithms, natural logarithms, base, logarithmic regression
7-35 odd
Chapter 4.4, P. 377-379
grapsh of logs, domain, inverse functions,
7-25 odd, 26-30, 31-33, 38-40, 59*, 60*
Chapter 4.5, P. 389
properties of logs, log(uv)=log u + log v, log(u/v)=log u - log v, log (b^c) = c log b, logb M = log M / log b
3-25 odd
Chapter 4.6, P. 399-400
5-27 odd, 31-35 odd, 37-49 odd, 65, 67,
Chapter 5.1, P. 455-456
measure of an angle, degrees, radians, conversions, quadrants, unit circle with angels,
unit circle with radians, Θ =s/r where s is arc length, sector area A= 1/2 Θ r^2, angular and linear speed, subtended
6-21, 22-25, 27-39 odd, 41, 43, 45, 47, 49, 51, 53, 55, 57, 58-61, 65*, 67.
Chapter 5.2, P. 470-472
sin and cosine functions, sohcahtoa
6-9, 10-22, 23-33, 34, 35, 37, 38, 39, 41-49, 51, 53, 55, 57, 59, 60-69, 72-76, 79, 91-99 odd, 100, 101.
Chapter 5.3, P. 484-485
tan, cot, sec, csc, fundamental identities, simplify trig expressions, alternate forms of the pythagorean theorem, period of a function
1, 6-17, 19-37 odd, 49, 51, 71, 74*.
Chapter 5.4, P. 495-497
solving triangles, angle of elevation, angle of depression,
7, 9, 11-31 odd, 43, 45, 47, 49, 51, 53, 55.
Chapter 6.1, P. 520-522
amplitude, period, midline, horizontal and vertical shifts, finding solutions of f(x)=sin x and g(x)=cos x
7-15 odd, 19, 20, 23-27 (* for equation), 31-36, 38-42, 48*
Chapter 6.2, P. 538-540
6-9, 10-16, 17, 19-33 odd, 39, 45,
Chapter 6.3, P. 550-551
8-16, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 35, 36, 37, 39, 43, 45, 47, 53, 55, 59, 61.
Chapter 7.1, P. 568-569
trid identities
5-15, 17-27 odd, 29-33 odd, 35, 37, 39
Chapter 7.2, P. 568-569
trid identities
5-17 odd, 21, 23, 47, 49, 51, 53, 55
Chapter 7.3, P. 594-595
trid identities
5-43 odd, 55-63 odd
Chapter 7.5, P. 594-595
trid identities
5-31 odd, 35, 39, 41, 42, 48, 51, 52, 53, 65, 85, 89,