Sec.
|
Problems
|
|
3.1 |
5. check denominators and even
roots 17. solve
equation for x 31. substitute
input for x 59. substitute
input in f(x) 61. solve
equation f(x) = g(x) for
x 73. see hint
for 3.1.31 83. determine f(ax
+ b) 85. substitute
input for t 87. substitute
input for x 93.
substitute input for x |
|
3.2 3.3 3.4 |
7. substitute cuberoot(3) for x 21. calculate
given values of f
and g first 22. (a) (b)
compare graphs of f
and g in domain;
(c) (d) substitute inputs for x 57. use
average rate of change formula for interval [1,b] 15. basic
graph is sqrt(x) 17. basic
graph is 1/x 19. basic
graph is x^3 27. 5 - x = -(x - 5) 29. y = -f(x - 5) + 1 61. draw a
point (a, b) in any
quadrant, e.g., Quadrant 1 63. expand
right side of equation 9. (a) calculate (k – h)(x) first 15. (a)
substitute (x +
1)/(x – 1)
for x in F(x) 19. compute
value of "inside" function first 31. find
"inside" and "outside" functions 51. g(a) = 2a - 1 |
|
3.5 |
13. (a) solve
equation for x 21. (a) find g^(-1)(x) for each of the three points plotted 45. (a) what
is f^(-1)(6)? 49. a point in
the graph of f is (x, f(x)); . a point in the graph of f^(-1) is (x,
f^(-1)(x)) 55. draw a
point (a, b) in any
quadrant, e.g., Quadrant 1 |
|
4.1 |
1. find the
coordinates of two points on the graph of the function 5. the slope
of f is the same as
the slope of x
– y = 1 9. find the
coordinates of two points on the graph of the function 16. (a) find
two points on the graph of the function, (c) y = x 23. (c) solve A(t) = B(t) 25. (a) find
the coordinates of two points on the graph of the function (you may let
(year) 1970 = 0) 43. (b) (c)
(d) compute composition first 49. compute
composition first |
|
4.2 4.5 4.6 |
5. determine
vertex first; x-intercepts
occur when y = 0, y-intercepts occur when x = 0 17. complete
the square 19. find the
vertex 27. find the
vertex 39. (a) (b)
find vertex of "inside" function 43. calculate f(x1) and f(x2) 45. factor an a from each term first 47. see hint
for 3.1.31 53. use
"vertex" form of parabola 55. find the
vertex 11. (b) find
the vertex 13. find the
minimum value of the distance function between the given point and a general
point on the graph of y 23. (a) use 2x
+3y = 6 to rewrite x^2 + y^2 as a function of x 28. (a) find
the minimum value of the distance function between the given point and a
general point on the graph of y 19. determine
translations, reflections, and dilations 23. (a)
determine sign of graph between adjacent x-intercepts 27. determine
sign of graph between adjacent x-intercepts 33. (b) see
example #4 on p. 246 37. (b) see
example #4 on p. 246 39. do not
estimate x-intercepts
from the graph 41. do not
estimate x-intercepts
from the graph 55. (a) draw a
right triangle from the center of the sphere to the center of the base and to
the point in the lower right of the cylinder where r meets h; (b) volume of a cylinder is equal to
the area of its base times height |
|
4.7 |
3. for
intercepts, x-intercepts
occur when y = 0, y-intercepts occur when x = 0 5. for
intercepts, x-intercepts
occur when y = 0, y-intercepts occur when x = 0 11. see
example 3 on p. 253 15. see
example 4 on p. 254 19. see example
5 on p. 255 23. consider
behavior of y for
large (absolute) values of x 25. see
example 8 on pp. 256-7 33. to find
point of intersection of graph and horizontal asymptote, set the two
equations equal to each other and solve 37b. what does
the graph of y look
like near x = 3? |
|
5.1 5.2 5.3 |
25. determine
translations, reflections, and dilations 27. determine
translations, reflections, and dilations 29. determine
translations, reflections, and dilations 31. determine
translations, reflections, and dilations 33. look for
common factors 39.f(x + h)
= 2^(x + h) 47. sketch
graph first 48. sketch
graph first 49. sketch
graph first 13. see
example 2 on p. 293 15. rewrite as
exponential equation 17b. see
example 4 on p. 293 23. see
example 5 on p. 294 33. see
example 7 on p. 294 53. e^(2x) = (e^x)^2 61. sketch
graph first 62. sketch
graph first 63. sketch
graph first 67. sketch
graph first |
|
5.4 5.5 5.6 5.7 |
49. see
example 6 on p. 305; 12 = 4 x 3 7. see example 4 on p. 312 29. see
example 2 on p. 311 31. see
example 6 on p. 314 37. see
example 6 on p. 314 75. solve for e^(-kx) firts 3. use formula on p. 322, solve
for r 13. use
formula on p. 325, solve for P 15. A = 1.06P 1. see example 1 on p. 332 13. see
example 1 on p. 332 23. see
example 4 on p. 336 27. see
example 4 on p. 336 57. see 5.7.52 |
|
6.2 6.3 6.4 |
61. use basic
right-triangle identities 11. draw
picture; find lengths of legs of right triangle 13. (b) solve
for half of base 25. find
distances from P
and Q to based of
altitude 31. P(cos (theta), sin (theta)), use right
triangles 33. use right
triangles 55. use
formula on p. 391 |
|
9.1 |
5. use Law of Sines 7. use Law of Sines 15. use Law of
Sines to find a and
b first 21. use Law of
Cosines 27. use Law of
Cosines 39. use Law of
Cosines 43. use Law of
Cosines |
|
6.4 6.5 7.1 7.2 7.3 7.5 |
63. h = sin (theta) 1. see example 1 on p. 395 or draw
right triangle 9. see example 2 on p. 396 17. use
formula (4) on p. 410 18. use
formula (4) on p. 410 35. see
example 8 on p. 414 37. see
example 8 on p. 414 39. see
example 8 on p. 414 11. find areas
of sector and triangle 19. see
example 4 on p. 420 37. (a) find
length of arc first 25. see
example 2 on p. 431 or draw
right triangle 29. determine
quadrant and draw right triangle 35. see example
4 on p. 432 37. see
example 6 on p. 433 55. draw right
triangle and determine sin(t)
and cos(t) 5. see example 2 on p. 455, but
use sine graph 23. see
example 6 on p. 458 25. see
example 5 on p. 457 27. y =- -cos(2x – pi/3) + 1 29. see
example 4 on p. 456 33. see
example 4 on p. 456 |
|
7.7 |
5. see example 2 on p. 470 9. see example 1 on p. 469, but
use cotangent graph 11. see
example 3 on p. 471 13. horizontal
translation 15. see
example 4 on p. 472 25. draw sine
graph first 27. draw
cosine graph first |
|
6.2 6.5 7.3 8.1 8.2 8.3 |
37. rewrite in
terms of sines and cosines 41. factor
numerator 43. find
common denominator 45. rewrite in
terms of sines and cosines; find common denominator 47. rewrite in
terms of sines and cosines 49. use basic
right-triangle identity 55. simplify
compound rational expression 21. rewrite in
terms of sines and cosines 23. rewrite in
terms of sines and cosines 25. rewrite in
terms of sines and cosines; use Pythagorean identity 27. rewrite in
terms of sines and cosines; simplify compound rational expression 29. rewrite in
terms of sines and cosines 31. rewrite in
terms of sines and cosines 33. rewrite in
terms of sines and cosines; use Pythagorean identity 35. rewrite in
terms of sines and cosines; use Pythagorean identity 37. rewrite in
terms of sines and cosines 47. rewrite in
terms of sines and cosines 49. find
common denominator; use the second Pythagorean identity 23. substitute
values for sin(pi/3) and cos(pi/3) 25. draw right
triangle or use Pythagorean identity to find missing trig values 31. draw right
triangle or use Pythagorean identity to find missing trig values 39. use
addition formulas for tangent 57. tan(2
theta) = tan(theta + theta) 59. delta f = f(x + h)
– f(x) and delta x = (x + h) - x 77.
cross-multiply; use addition formulas for sine 7. use half-angle formulas 11. (a) use
double-angle formulas on p. 492; (b) use double-angle formulas on p. 495 27. see
example 2 on p. 494 39. see
example 4 on p. 495 43. factor
right side of equation 25. use a
sum-to-product formula |
|
8.4 8.5 |
3. see example 1 on p. 507 15. see
example 3 on p. 511 17. see
example 3 on p. 511 19. see
example 5 on p. 512 21. add sqrt(1
+ sin^2(t)) to both
sides and square both sides of equation 45. see
example 7 on p. 513 56. (a) use
Pythagorean identity 5. see example 8a on p. 525 11. see
example 4d on p. 521 19. see
example 6b on p. 523 21. see
example 10 on p. 525 33. use
addition formula for cosine 37. see
example 9 on p. 525 57. take sine
of both sides of equation |
|
9.2 9.3 |
27. see
example 2 on p. 556 37. see
example 3 on p. 556 43. see
example 4 on p. 557 47. see
example 5 on p. 558 11. see
example 2 on p. 562 19. see
example 3 on p. 564 29. see
example 3 on p. 564 37. add
vectors in component form first 41. see
example 5b on p. 565 47. see
example 6 on p. 565 51. see
example 7 on p. 565 61. (b)(c)(d)
use definition of dot product on p. 567 65. use cosine
formula on p. 567 |
|
3-D 9.5 9.6 |
Supplement 1. see example 1 on p. 578 4. use formulas on p. 577 9. tan (theta) = sin (theta)/cos
(theta); see example 2a on p. 578 11. see
example 2b on p. 578 13. multiply
both sides of equation by denominator 15. use
addition formula for cosine 17. see
example 3 on p. 579 21. see
example 3 on p. 579 23. see
example 3 on p. 579 31. see
example 4 on p. 579 37. see
example 5 on p. 580 41. see
example 7 on p. 582 3. see example 1 on p. 586 9. see example 2 on p. 587 13. see
example 3 on p. 588 15. see
example 4 on p. 590 21. use
symmetry tests on p. 587 23. use
symmetry tests on p. 587 27. use
symmetry tests on p. 587 |
|
13.6 |
5. see example 1 on p. 855 11. see
example 2 on p. 855 23. see
example 3 on p. 856 31. see
example 4a on p. 857 37. see
example 4b on p. 857 45. see
example 6 on p. 857 69. see
example 8 on p. 859 |
|
10.1 10.2 10.3 |
31. see
example 5 on p. 605 33. see
example 6 on p. 606 37. write two
equations: one for weight, one for cost 39. multiply
both sides of both equations by ab 61. use
substitution to solve for y 62. use
addition-subtraction method 31. (a)
substitute three pairs of points into equation to write the equation in A, B, and C 33. substitute
three pairs of points into equation to write the equation in A, B, and C 35. substitute
three pairs of points into (x
– h)^2 + (y – k)^2 = r^2 to solve for h, k, and r, then convert to desired form 11. see
example 3 on p. 622 15. see
example 3 on p. 622 17. see
example 3 on p. 622 21. see
example 3 on p. 622 39. see
definition of matrix addition on p. 623 45. see Table
3 on p. 628 53. see example
6 on p. 628 |
|
10.4 |
29. see
example 2 on p. 634 35. (a)
compute A^(-1) and B^(-1) first |
|
10.5 10.6 10.7 |
5. use definition of 2 x 2 determinant on p. 639 19. see
example 2 on p. 642 27. see
example 4 on p. 644 29. see
example 4 on p. 644 35. see
example 5 on p. 645 37. see
example 5 on p. 645 39. see
example 5 on p. 645 3. see example 2 on p. 652 5. see example 3 on p. 653 7. use addition-subtraction method 8. use substitution method 15. use
substitution method 21. use
substitution method and write terms in base-2 37. write two
equations: one for area, one for sides 1. substitute values into
inequality 17. see
example 2 on p. 660 23. see
example 2 on p. 660 25. see
example 2 on p. 660 27. see
example 2 on p. 660 29. see
example 2 on p. 660 |
|
Conics |
Supplement |
|
2.1 11.2 11.4 11.5 |
23. see
examples 5 and 7 on pp. 39 and 41 45. find the
radius of the circle 47. find the
radius of the circle 51. find the
center of the circle first, then find its radius 21. see
example 5 on p. 687 25. draw
picture, determine p 27. draw
picture, determine p 29. draw
picture, determine p,
see Figure 9 on p. 686 13. see
example 4 on p. 700 21. see
example 4 on p. 700 25. draw
picture, determine orientation of ellipse, determine form of equation 27. draw
picture, determine orientation of ellipse, determine form of equation 29. draw
picture, determine orientation of ellipse, determine form of equation 31. draw
picture, determine orientation of ellipse, determine form of equation 32. draw
picture, determine orientation of ellipse, determine form of equation 45. solve
system of equations 11. see
example 2 on p. 715 21. see
example 2 on p. 715 27. draw
picture, determine orientation of hyperbola, determine form of equation 29. draw
picture, determine orientation of hyperbola, determine form of equation 31. draw
picture, determine orientation of hyperbola, determine form of equation |
|
12.1 12.2 12.3 |
61. (a)
compute z^2 first,
then multiply by z 71. find
common denominator 25. see
example 4 on p. 765 37. see
example 4 on p. 765 45. see
example 4 on p. 765 49. see
example 3 on p. 764 13b.
substitute value for x 15. see
example 2 on p. 767 19. see
example 3 on p. 769 45. see
example 7 on p. 772 55. (a) use
synthetic division given one of the roots is equal to -5 57. substitute
value for x |
|
12.4 12.5 12.6 |
1. see example 1 on p. 776 2. see example 1 on p. 776 5. see example 2 on p. 777 11. see
example 3 on p. 779, multiply out 14. see
example 3 on p. 779, multiply out 19. see
example 4 on p. 779 15. use of
Upper and Lower Bound theorem not required 19. use of
Upper and Lower Bound theorem not required 21. use of
Upper and Lower Bound theorem not required 25. use of
Upper and Lower Bound theorem not required 9. see example 1 on p. 793 13. see
example 1 on p. 793 15. see
example 1 on p. 793 39. see
example 3 on p. 795 |
|
12.7 12.8 |
5. see example 2 on p. 800 7. see example 2 on p. 800 13. see
example 3 on p. 802 17. use either
method (though convenient values is probably easier) 19. use either
method 21. use either
method 11. see
example 5 on p. 810 29. see
example 5 on p. 810 |
|
13.3 13.4 13.5 |
13. see
example 1 on p. 838 15. see
example 3 on p. 839 27. see
example 2 on p. 839 49. see
example 5 on p. 841 53. see
example 6 on p. 842 9. see example 4 on p. 848 19. see
example 4 on p. 848 23. see
example 4 on p. 848 25. see
example 5 on p. 849 13. see
example 3 on p. 852 15. write each
term, then use formula for sum of a geometric series 19. see
example 4 on p. 853 |
|
2-var fns |
Supplement |