# Errata for Precalculus: An Investigation of Functions

**Precalculus: An Investigation of Functions**

**Errata to Edition 2.3**

**Errata to Edition 2.2**

**Chapter 1**

- 1.3, Exercise 9. The question isn't reasonable since the interval spans a discontinuity.
- 1.3, Page 43. The two graphs above the callout box about Concavity are in the wrong order. The concave down graph for Company A is showing second when it should be first.

**Chapter 3**

- 3.2, exercise 1: Wrong graph (doesn't match answers in back, and missing grid).
- 3.4, example 5. Under the synthetic division lines, the first factorization should be `(x-1/2)(4x^3-2x^2-12x-6)` . The current expression is missing the 12.
- 3.7, example 4. The statement "the vertical asymptotes occur when the denominator is undefined" is not accurate; it's when the denominator is zero, causing the expression to be undefined.
- 3.7, page 222, def of asymptotes: the statement "vertical asymptotes occur when the denominator is zero and the numerator is not zero" is not true if a factor in the denominator has higher multiplicity.

**Chapter 6**

- 6.5, page 445: The link in the footnotes no longer works. A replacement is https://www.desmos.com/calculator/bmc9whd6in

**Chapter 7**

- 7.1, exercise #9, the answer in the solutions is listed as 0.1339+10k, but it should be 1.3386+10k
- 7.1, exercise #11, the listed solutions are incorrect. They should be t=-0.0966 + 2pi/3 k and t=1.1438 + 2pi/3 k
- 7.2, exercises 21 and 22 are identical aside from variable.

**Chapter 8**

- 8.5, example 2, cos(150deg) should be `-sqrt(3)/2` , so the answer should be `-21 sqrt(3)`

**Chapter 9**

- 9.1: example #4, the general form of the equation should have a (y-k) not a (h-k)
- 9.1: example #2, the final equation should be `x^2/14^2 + y^2/8^2 = 1`
- 9.1: example #6, the second line under the figure should have b=20 rather than 15 in the equation.
- 9.2, example #5, the general equation should have a (y-k) not (h-k)
- 9.3, example 5, the third line from the bottom should be `9u^2-u-9`

**Errata to Edition 2.1**

Some sections have the wrong page header, like 3.8 Exercises.

**Chapter 1**

- 1.6, page 94, the sentence below Try it Now 1 is missing a word: "Notice that the original function and the inverse function..."
- 1.5, page 78 Ex 18, the graph compression does not match the compression and points described in the text. The graph actually shows a 1/2 compression, when it should have shown a 1/3 compression.
- 1.6, Try it Now Answer #1, should be h(2)=6 rather than g(2)=6.
- 1.3, Example 9. Second graph should be from a TI calculator or other tool

**Chapter 2**

- 2.4: The calculator linked at the bottom of page 140 does not produce accurate results.

**Chapter 3**

- Solutions manual, 3.3 #51: The statement about "dividing the y-value by the x-value gives the height of the rectangle" is incorrect. Either divide the area by 2x, or just plug the x-value into the parabola equation to get y=3.336, which is the height of the rectangle.
- 3.4, page 200, example 5: The result of the first synthetic division is incorrect; it should be 4 -2 -12 6 0, which would then be the first line of the next synthetic division. The final result is correct.

**Chapter 4**

- 4.1, page 250, below the table. "each year the company is grows by 50%" should read "each year the company grows by 50%".
- 4.2, page 274, Try it Now 2 answer should be `y=2e^(-x)+4` , not `y=-2e^x+4`
- 4.4, page 294, Example 7, In the first line of the section set of equations, it should be ln(4x+14) not ln(4x+13). Later, the factorization should be (x-4)(x+3) with solutions x=4 and x=-3.

**Chapter 5**

- 5.1, page 343, exercises 7&8. The language should be clarified to say that the points lie at the ends of the diameter.

**Chapter 6**

- 6.1, page 401, example 4. the line "Normally we would express the x coordinate of a point on a unit circle using x=rcostheta" should read "Normally we would express the x coordinate of a point on a circle centered at the origin using x=rcostheta"
- 6.4, page 434, example 6. The angle in the picture should be labeled -62.7, not -67.7

**Chapter 7**

- 7.3, page 672. solution to 7.3#23. Signs are off. Solution should be `1/16 - 1/16 cos(2x) - 1/16 cos(4x) + 1/16 cos(2x) cos(4x)`
- 7.4, page 492, example 4. The first line should start "A spring with natural length of 20 feet" rather than "A spring with natural length of feet inches"

**Chapter 8**

- 8.4: Try it Now Answers are misnumbered.

**Chapter 9**

- 9.2 Example 2: asymptote changes from 4/3x to 3/4x
- 9.3 Example 10 should be numbered Example 6

**Errata to Edition 2.0**

**Chapter 1**

- 1.2 (page 23): footnote link is broken
- 1.5, top of page 73, the first two graphs are in the wrong order

**Chapter 2**

- 2.1: Footnote link doesn't work
- 2.4 ex#8: the r should be positive since the slope is positive

**Chapter 3**

- 3.1, terms of poly functions. "positive whole number power" should be "non-negative whole number powers" (and yes, I know that's redundant), and "transformed power function" should be "vertically stretched or compressed power function"
- 3.3, solutions manual: #5: third x-intercept should be (1,0) not (-1,0)
- 3.7, example #12, the oblique asymptote is -x+3, not 2x+1.
- 3.7, HW #10 is missing an x in the denominator (should be 14x, not 14)

**Chapter 5**

- 5.5, the answer for #1 has the values for sec and csc swapped.

**Chapter 6**

- 6.1, the selected answers include the answers to the evens.

**Chapter 9**

- 9.1, graph of the horizontal ellipse at the bottom of page 582: The foci were swapped: (-c,0) should be on the left, and (c,0) on the right.
- 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 x=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 sin
^{2}(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`