Precalculus: An Investigation of Functions

Errata to Edition 2.0

Chapter 3

  • 3.7, example #12, the oblique asymptote is -x+3, not 2x+1.

 Chapter 9

  • 9.3 Exercise #7, the answer in the back was incorrect. The directrix is y=-1/8 and the focus is (0,1/8)
  • 9.3 Exercise #9, the answer in the back was incorrect.  The directrix is y=1/16 and the focus is (-1/16,0)

Errors in Older Editions

Errata to Edition 1.5

Chapter 1

  • In 1.1 Example 8, the description for Graph one should say "For example, the output value 3 has two corresponding input values, -1 and 2.3".   (Thanks Gerard)

Chapter 2

  • In 2.4, Try it Now #4, the answers should include equality:  `k le 1 or k ge 7` ,  `(-oo,1]uu[7,oo)` 

Chapter 8

  • In 8.5, Try It Now #3, the radius is `sqrt(3)`  so the equations should be `x(t) = sqrt(3)cos(t)`  and `y(t)=sqrt(3)sin(t)` 

Errata to Edition 1.4

Chapter 3

  • The solution for 3.3 #25 should be `(-oo,1]uu[4,oo)` 

Chapter 7

  • Exercise 26 isn't possible.  It should read 270 < x < 360.

Chapter 8

  • Example 7:  This incorrectly states that solving `cos(theta)=1`  gives `theta=0`  or `theta=pi` .  The correct explanation is:  At `theta=0` , `r=4cos(0)=4` , putting us at the Cartesian point (x,y) = (4,0).  From `theta=0`  to `theta=pi/2` , `r=4cos(theta)`  is positive, giving points in the first quadrant.  At `theta=pi/2` , r=0 putting the graph at the origin.  From `theta=pi/2`  to `theta=pi` , `r=4cos(theta)`  is negative, giving Cartesian coordinates in the 4th quadrant.  At `theta=pi` , `r=4cos(pi) = -4` , returning us to the Cartesian point (x,y)=(4,0), back where we started.  From here the graph repeats from `theta=pi`  to `theta = 2pi` .` ` ` ` ` ` 

Errata to Edition 1.3

Chapter 1

  • Section 1.1
    • The second paragraph had the quantities reversed.  It should read: "if we tried to reverse that relationship and determine age from a given height"
  • Section 1.3
    • Problem 26 doesn't make sense, as it's not monotonic.  Outputs should be:  90, 80, 75, 72, 70.
    • The solution to #37 should list (0,5) as an additional inflection point.

Chapter 3

  • Section 3.2
    • #39, the linear term of the equation should be 4/5 x, not 45 x.  
  • Section 3.3
    • The answer for #27 should be [-2,-2]U[3,infinity)
  • Section 3.4
    • Page 196, the third graph on the page is incorrect - it does not match the function.

Chapter 7

  • Section 7.1
    • The second solution to #37 should be 2pi/3, not pi/3
  • Section 7.2
    • There are two questions numbered 44.  Since the detailed solutions created by Shoreline already have solutions to the "odds", we'll probably address this in future editions by removing the second question currently numbered 44, so the "Prove the identity" section will begin with #45.
    • Page 420, example 3.  The second to last line of the example, on the top of page 420, has a typo.  It should read `=(sin(a)cos(b)+sin(b)cos(a))/(sin(a)cos(b)-sin(b)cos(a))` 
  • Section 7.3
    • The last solution to #17 should be `(4pi)/3` , not `(4pi)/93` 

Errata to Edition 1.2

Chapter 1

  • Section 1.1
    • Solution for exercise #23 should be f(0) = 3, not 34.
  • Section 1.4
    • Solution for exercise #29b shold be (-oo,-2)U(2,oo)

Chapter 2

  • Section 2.1
    • Solution to #5 should be 40 - 2n

Chapter 3

  • Section 3.2
    • Solution for exercise #17 should be b=32, c = -39
  • Section 3.4
    • The solution to #31 should be `(-6(x-1)^2)/((x+3)(x-2)^2)`
  • Section 3.5
    • The important topics should list "Radical functions" not "rational functions"

Chapter 7

  • Section 7.3
    • The half-angle identity for cos was incorrectly written with a -1 right above Try it Now 4.  This mistaken form was then used in Example 7.
    • Answer to #21 should end with +1/8cos(32x), not -

Chapter 8

  • Section 8.1
    • Exercise #43:  The answer should be 7.72
  • Section 8.5
    • Exercise #1 and #2:  The correct graph is not shown
    • Exercise #35:  The equation for x(t) should be x(t) = -1+3t

Errata to Edition 1.1

Chapter 2

  • Section 2.1
    • Pg 105,  Try it Now states that a represents the amount withdrawn each quarter, but it should represent the number of quarters.
    • Pg 109, #32 is missing an = after the E(t).
  • Section 2.3
    • Exercise 3, the solution to part a should be C(x) = 0.15x + 10

Chapter 4

  • Section 4.4
    • Example 6, the growth rates for both countries were incorrectly written as 0.264 and 0.224 instead of 0.0264 and 0.0224 respectively.  The answer should 16 years.
  • Section 4.6
    • Example 5, the answer is 3.802 months (not years)
    • Orders of Magnitude, above example 10, should read "how many orders of magnitude A is greater than B"

Chapter 7

  • Section 7.3
    • Pg 434 Try it Now #2:  Should say sin2(75°) rather than sin(75°)

Chapter 8

  • Section 8.1
    • Pg 462 Exercise #7:  The rightmost side of the triangle should have length 18, not length 1.
  • Section 8.3
    • Solution to exercise #65 is incorrect.  Should be 1.149, .355+-1.092i, -0.929+- 0.675i
  • Section 8.4
    • Pg 500 TIN Answer #4:  Magnitude should be 88.73 ft.

Errata to Edition 1 (first printing)

Chapter 2

  • Section 2.1
    • Example 7:  The example would be more clear if the first sentence was worded as "Working as an insurance salesperson, Ilya earns a base salary and a commission on each new policy, so Ilya’s weekly income, I, depends on the number of new policies, n, he sells during the week." 
    • Flashback:  Should say "Looking at Example 7" rather than "Looking at Example 6"
  • Section 2.3
    • Homework problems #1 and #2 should state "assume the population is changing linearly"
  • Section 2.4
    • The discussion around correlation coefficient incorrectly suggests that the correlation coefficient tells us how linear the data is, rather than measuring the strength of a known linear relation.

Chapter 6

  • Section 6.1
    • Example 9:  The question does not specify that the equation should be a function of time in minutes, although it is implied by the units of the period.
  • Section 6.3
    • Example 3:  Correctly states that the cosine should be used, but then incorrectly uses the sine.  It should read `cos(theta)=9/12` , `theta = cos^-1(9/12)` , so `theta ~= 0.7227` , or about 41.4096°
    • Example 5 incorrectly states that `+-sqrt(9/5) = +- 3/4` .  It should instead state that `+-sqrt(9/25) = +- 3/5` .  The final answer to the example is then `3/5`

Chapter 7

  • Section 7.3
    • Example 6:  At step, 6, where it says to Simplify, the fraction 1/4 incorrectly becomes a 1/2.  It should not, and the constant in the final answer should be 3/8 not 5/8

Chapter 8

  • Section 8.1
    • Example 3:  The angle 48.3438 mistakenly becomes 43.3438 later in the example.  This will make the second angle 46.6562 degrees, and the final answer will be 8.7603

Solutions to Selected Exercises

  • Section 1.1
    • #29:  The solutions should be -4, -6, -6, -4, and 0.
    • #33:  f(-1) should be 1/2
    • #47a: f(c) = t  (t is the y-coordinate of the point L)
  • Section 1.2
    • #29:  The domain on the first piece (2x+3) should be `-3 le x < -1`
  • Section 1.4
    • #41b:  There are two possible solutions:  `g(x)=x sqrt(6) - 8/(sqrt(6)+1)`  and `g(x) = -x sqrt(6) - 8/(1-sqrt(6))`
  • Section 1.5
    • #97:  `y = root(3)(-1/2(x-2))+1`
  • Section 3.4
    • #17:  The y-intercept is (0, -15/16).  The graph for #17 is correct.
  • Section 4.4
    • #15 is missing the log:  `log((xz^3)/sqrt(y))`
    • #43: There are two valid solutions:  `3 +- sqrt(15)` , or approximately 6.873 and -0.873
  • Section 4.7
    • #11:  `y = 731.92(0.738)^x`
  • Section 5.4
    • #11: The values for sec and csc are reversed.  `sec(theta)=-3, csc(theta) = -(3 sqrt(2))/4`