# DIFFERENCES BETWEEN WEB and PRINT VERSIONS

Occasionally, I make minor changes to my web lessons, that aren't reflected in my printed books.
In the online lessons, attention is drawn to added material by a purple dashed outline.
Errata are corrected in the online lessons and indicated here.
Such differences between online and printed versions are listed below.
 DATE WEB LESSON CHANGE July 21, 2021 Length of a Circular Arc (and Related Concepts) Change ‘Degees’ to ‘Degree’. July 21, 2021 Review of Circles (and Related Concepts) Typo: change $\,r\,$ to $\,r^2\,$ in definition of interior of circle. July 17, 2021 Graphing Generalized Sines and Cosines Correct repeated word: ‘the period is the the horizontal...’; July 10, 2021 Fundamental Trigonometric Identities Add in missing words: the terminal point for $\,t\,$ ... June 6, 2021 The Trigonometric Functions Remove (missing) link to Drexel (Ask Dr. Math). June 5, 2021 Doubling Time, Half-Life Change ‘$\,b < 1\,$’ to ‘$\,0 < b < 1\,$’ in three places. June 4, 2021 Solving Exponential Growth and Decay Problems Change ‘alternate’ to ‘alternative’ in four places. Reformatting: move the ‘Yuck!’ to be centered in a new row at the bottom. Change ‘solutions steps’ to ‘solution steps’. Fix typo: $P(3\Delta t) = b\cdot P_{\,0}b^2 = P_{\,0}b^3$ (change $\,1\,$ to $\,2\,$ in exponent) June 2, 2021 Solving Exponential Equations Change ‘There are NOT ExpTerms’ to ‘These are NOT ExpTerms’. Change ‘Solve (continued)’ to just ‘Solve’. May 27, 2021 Logarithmic Functions: Review and Additional Properties Change two occurrences of ‘alternately’ to ‘alternatively’. May 23, 2021 Simple Versus Compound Interest Change ‘compounding periods per years’ to ‘compounding periods per year’. May 15, 2021 Introduction to Average Rate of Change Change ‘alternately’ to ‘alternatively’. Change ‘sometime downhill’ to ‘sometimes downhill’. May 15, 2021 The Natural Exponential Function Formatting change, to agree with the text ‘Clearly, the numbers in the right-hand column at left’. May 8, 2021 Exponential Functions: Review and Additional Properties Change ‘alternately’ to ‘alternatively’ (two places). May 8, 2021 Introduction to Puncture Points (Holes) Remove the word ‘it’ in ‘it isn't defined’. April 26, 2021 Introduction to Rational Functions Change ‘alternately’ to ‘alternatively’. April 26, 2021 Solving Polynomial Equations Two typos: replace $\,x^2\,$ with $\,x\,$ in Step 5 of example; change ‘and real numbers’ to ‘are real numbers’. April 22, 2021 Multiplying and Dividing Fractions with Variables Change first occurrence of ‘puncture point’ to a link (suggestion from Ray). April 11, 2021 Greatest Common Factor of Two or Three Numbers Mistake: removed entire section titled ‘BONUS: An Efficient Algorithm for Finding the Least Common Multiple’ Also removed link to this section in Finding Least Common Multiples. I have un-published the two Algebra I web books until I decide how I want to address this. April 11, 2021 Arithmetic with Complex Numbers Typo: change ‘$\,31\,$’ to ‘$\,3i\,$’ March 20, 2021 Turning Points of Polynomials Typo: change ‘$\,x\le 3\,$’ to ‘$\,x\le c\,$’ March 20, 2021 Finding Inverse Functions (switch input/output names method) Typo: change ‘which is output from’ to ‘which is an output from’ Typesetting fix: change left single quote to right single quote on the word ‘simple’ March 17, 2021 Finding Inverse Functions (when there's only one $\,x\,$ in the formula) Clarification: change ‘Here's one. The other is similar.’ to ‘Here's one proof. The other proof is similar.’ March 2, 2021 Max/Min Problems Resulting in Quadratic Functions Typos: Insert missing minus signs in $\,\left(-\frac{b}{2a},f(-\frac{b}{2a})\right)\,$ in two places; Re-format ‘Suggested Review’ at beginning (bullets don't work well next to the mathematical cat) February 26, 2021 Piecewise-Defined Functions Typo: Add a missing space, ‘quadratic,since’. February 22, 2021 Basic Function Models You Must Know Typos: change two ‘the the’ to ‘then the’. For exponential functions, change ‘if $\,x = 100\,$’ to ‘if $\,y = 100\,$’. February 13, 2021 Sketching Regions in the Coordinate Plane Change ‘alternately’ to ‘alternatively’. February 8, 2021 Review of Lines and Slopes of Lines Change ‘times as fast than the inputs’ to ‘times as fast as the inputs’. Remove section linking to user exercise on lines; no longer working. February 2, 2021 Absolute Value as Distance From Zero Typos: in two places, change ‘on one side of the equation’ to ‘on one side of the inequality’ February 2, 2021 The Test Point Method for Sentences Like ‘$\,f(x) \gt g(x)\,$’ Typo: change ‘to indicate than’ to ‘to indicate that’ January 31, 2021 The Test Point Method for Sentences Like ‘$\,f(x) \gt 0\,$’ Typo: change ‘to indicate than’ to ‘to indicate that’ January 13, 2021 Parallel and Perpendicular Lines Add the word ‘distinct’ in two places. January 1, 2021 Quadratic Functions and the Completing the Square Technique Typos: change ‘can be real number’ to ‘can be any real number’; change ‘hold water’ to ‘holds water’; change $\,a(h-k)^2 + k\,$ to $\,a(x-h)^2 + k\,$; change $\,-\frac{20}{29}\,$ to $\,-\frac{29}{20}\,$ December 30, 2020 Equations of Simple Parabolas Typo: change ‘the the parabola’ to ‘then the parabola’ December 27, 2020 Parabolas Typo: change ‘parabola nets narrower’ to ‘parabola gets narrower’ November 30, 2020 Simple Word Problems Resulting in a System of Equations Change ‘in the following example’ to ‘with the following example’. November 30, 2020 Measures of Spread Typo: replace $\,x_1\,$ with $\,x_i\,$ in the sentence beginning ‘A reasonable idea is to...’. November 14, 2020 Advanced Set Concepts Replace ‘alternately’ with ‘alternatively’. November 9 and 11, 2020 Composition of Functions , Graphical Interpretations of Sentences Like $\,f(x) = g(x)\,$ and $\,f(x) > g(x)\,$, and Graphical Interpretations of Sentences Like $\,f(x) = 0\,$ and $\,f(x) > 0\,$ Typos: change ‘Graphs of Function’ to ‘Graphs of Functions’ in beginning link November 7, 2020 Basic Models You Must Know Typos: change ‘Graphs of Function’ to ‘Graphs of Functions’ in beginning link; changed ‘dom’ to ‘ran’ for cubing function; correct symbolic statement of domain for absolute value function; change ‘functions’ to ‘function’: ‘Every constant functions graphs as...’ November 2, 2020 Compound Interest Formula Typo: changed ‘years’ to ‘year’ (singular) in the Compound Interest Formula box. October 29, 2020 Arithmetic and Geometric Sequences Changed 12 to 12.5 (twice) in geometric series example. October 19, 2020 More on Exterior Angles in Triangles Changed ‘with respect to $\,\angle C\,$’ to ‘with respect to the exterior angle at $\,\angle C\,$’. October 17, 2020 Practice with Two-Column Proofs Typo (two places): change ‘REASONS columns’ to ‘REASONS column’ (singular). October 11, 2020 Relationships Between Angles and Sides in Triangles Typo: changed ‘$\,B\Leftarrow A\,$’ to ‘$\,A\Leftarrow B\,$ (that is, $\,B\Rightarrow A\,$)’. October 11, 2020 Triangle Congruence Changed ‘alternately’ to ‘alternatively’. October 11, 2020 Angles: Complementary, Supplementary, Vertical, and Linear Pairs Removed the cursor from the vertical angle image. October 3, 2020 Introduction to the Two-Column Proof Typo: changed ‘in written in’ to ‘is written in’. October 3, 2020 Proof Techniques Typo: changed ‘the only time than an’ to ‘the only time that an’. September 28, 2020 Quadrilaterals Changed ‘containing’ to ‘connecting’ in the definition of convex; much clearer. September 19, 2020 More Practice with Function Notation Missing factor of $\,2\,$ in displayed equation; corrected in online (not print) version. September 14, 2020 Finding Slant Asymptotes Added a ‘real-life’ example of a slant asymptote to online version, per user request. September 14, 2020 Finding Vertical Asymptotes Added ‘real-life’ examples of vertical asymptotes to online version, per user request.