PreCalculus (2017 – 2018)

Welcome! Lesson details for each day are described below.  I will do my best to not only stay updated, but also provide extra links and resources for you to use and explore.  My Channel for Precalculus

Helpful Tutor:  Drew Laiche (  Advanced Math Tutor.

End of year survey:

Pamphlet for next year:  In order to help the next class of PreCalculus students, we will make a pamphlet to show them what to look for.  We will focus on two areas:  math content and study skills.  You should provide advice regarding study skills and also advice on specific content you’ve encountered this year.

The pamphlet will be completed in class with a group.  Out of the 6 panels the pamphlet has, 3 will be for study skills and 3 will be for math content.

End of Year Review

Final Exam Days:  May 29th and May 31st (Senior’s last week)

*Following the final exam for all non-seniors, we will preview a few calculus concepts*

Day 77:  May 29th.  Objective:  Students will prove their knowledge by completing part 1 of the final exam.  Formula Sheet:  Trig_Cheat_Sheet_Reduced – Make sure to write down the half-angle formulas! Half-AngleFormulas  STAMPS: You should get that stamped prior to class on May 29th. You should have 3 stamps total.

Day 76:  May 24th.  Objective:  Students will review the vectors and parametric equations portion of the final review.  Final Review Keys:  PC2ndSemReviewFinalKEY (vectors and parametric equations)   PC5-ReviewTest(3)KEY (Analytic Trigonometry) PC4-Review2KEY (Trigonometry)

Day 75:  May 22nd.  Objective:  Students will plan for the final exam by reviewing semester material.  Homework:  PC2ndSemReviewFinal

Day 74: May 18th.  Objective:  Students will work collaboratively to complete the second trigonometry unit review.  Class work and Homework assignment:  PC5-ReviewTest(3) Key:  PC5-ReviewTest(3)KEY

Day 73:  May 16th.  Objective:  Students will complete a review for the second trigonometry unit to prepare for the final exam.  Class work and Homework assignment:  PC5-ReviewTest(3) Key:  PC5-ReviewTest(3)KEY

Day 72:  May 14th.  Objective:  Students will analyze the second trigonometry unit and form questions to prepare for the final exam.  Homework:  PC5-ReviewTest(2) Review Key:  PC5-ReviewTest(2)KEY

Day 71:  May 10th.  Objective:  Students will compile a list of questions on the first trigonometry unit.  Homework:  Complete the review PC4-Review2 Review Key:  PC4-Review2KEY

Day 70:  May 8th.  Objective:  Students will complete a group test to review for the trigonometry portion of the final exam. Jigsaw:  Jigsaw Study Session1 Review Homework:  PC4-Review2

Unit 9:  Conic Sections/Parametric Equations

Day 69:  May 4th.  Objective:  Students will demonstrate their comprehension of parametric equations by completing a unit test.  Test today.  

Day 68:  May 2nd: Objective:  Students will collaborate to review unit material in order to prepare for a unit test.  Review: PC Test review Key:  PC9Review Homework:  Complete the review and study for the test on Friday!

Day 67:  April 30th. Objective:  Students will graph parametric equations, convert them into implicit equations and construct diagrams in order to determine outcomes for a given physical scenario. Notes:  PC9-2Notes Homework:  p. 736 #’s 1, 7, 13, 26, and 27.  Don’t forget to complete each part of the problem (read the instructions).  Test on Friday!

Day 66:  April 24th.  Objective:  Students will review for the semester final and complete the Smarter Balanced Assessment.  Review:   PC4-Review2

Period 1:  Juniors taking the SBAC – report to SS 220

Non-Juniors/Non-Testers:  Report to Mr. Trotter’s room S-158

Period 2:  Everyone report to SS 220

Period 3:  Juniors taking the SBAC – report to SS 220

Non-Juniors/Non-Testers:  Normal Classroom (S-028)


Day 65:  April 20th.  Objective:  Students will locate and graph the center, foci, vertices, and asymptotes where appropriate given the equation of an ellipse or hyperbola.  Notes:  PC9-1Notes Homework:  PC9-1PracticeProblems

Unit 8:  Vectors

Day 64:  April 18th.  Objective:  Students will prove their knowledge by completing a unit test on vectors.  Test Today.  

Day 63: April 16th. Objective:  Students will apply their knowledge of vectors by completing a practice test.  Review: PC8-Review Review Key: PC8-ReviewKey Homework:  Make a notecard for the test on Wednesday.  You will not actually use it on the test, but your homework is to make one as if you would be able to.  Test Wednesday!

Day 62:  April 11th.  Objective:  Students will resolve vectors and apply them to a real life problem.  Class Problems:  8.4Vector Application Practice Homework:  p. 650 #’s 1-9 odd, 19, 20, and 21.  Make sure to draw diagrams and solve for the last three problems.

Day 61:  April 9th.  Objective:  Students will calculate the angle between vectors and apply vector components to physics problems.  Notes:  PC8-3Notes Practice:  PC8-3ApplicationPractice Class Problems:  PC8-3PracticeProblems Homework:  From the classwork worksheet:  PC8-3PracticeProblems do problem #’s 53-67 odd and #’s 79-82 ALL.

Day 60:  April 5th.  Objective:  Students will calculate unit vectors and resolve vectors. Notes:  PC8-2Notes Practice Problems:  PC8-2Practice Notebook Scans:  PC8-2PracticeNotes1of2 and PC8-2PracticeNotes2of2 Homework:  p. 641/642 #’s 39-43 odd, 49, 50, 51, and 52.

Day 59:  April 3rd.  Objective:  Students will find position vectors and perform arithmetic on vectors. Notes/Practice:  PC8-1Notes:Practice Homework:  p. 641 #’s 1-7 odd, 19-25 odd, 27-37 odd.

Unit 7:  Polar Coordinates

Polar Graph Results:

Period 1:  Class Picture

Period 2:  Class Picture

Day 58:  March 23rd.  Objective:  Students will create a series of polar equation graphs.  Project:  Using Desmos, create polar equation graphs to make artwork of your own.  Spend about 45 minutes on the work, submit it by e-mailing me the link, or sharing it via google doc – Project Rubric:  PC7-ProjectRubric

Day 57: March 21st  Objective:  Students will convert between polar and rectangular coordinates.  Notes: PC7-1Notes Homework:  p 600 #’s 21-29 odd, #’s 37 – 45 odd.

Unit 6:  Applications of Trigonometry

Day 56: March 19th.  Objective:  Students will demonstrate understanding of applications of trigonometry by completing a group test.  Homework:  none

Day 55:  March 15th.  Objective:  Celebrate pi-day.  Homework:  none

Day 54:  March 13th.  Objective:  Students will apply the law of cosines and law of sines to trigonometry application problems.  Class work:  PC6-3WordProblems Homework: Complete problems # 7 and #9 from the classwork problems: PC6-3WordProblems.  Tomorrow we celebrate pi day!  

Day 53: March 9th.  Objective:  Students will apply the law of cosines and law of sines to trigonometry application problems.  Homework:  G 7-5 Law of Cosines and Sines with notes

Day 52:  March 5th. Objective:  Students will solve application problems using right triangle trig.  Students will apply the law of sines to find missing sides and angles in non-right triangles. Homework:  Law of Sines

Unit 5:  Analytic Trigonometry

Day 51:  March 1st. Objective:  Students will review unit material. Review:  PC5-ReviewProblems  KEY!!!!  PC5-ReviewKey  Test is on Monday March 5th.  

YouTube Links:  (Keep in mind I may show things differently than I have in class.  Rationalizing denominators is one of those topics, so e-mail any questions you’ve got)

1) Identities

2) Solving Trig Equations Part 1 and Solving Trig Equations Part 2

3)  Sum and Difference Formulas (Look at thePC5-MidUnitReview as well) PC5-MidUnitReviewSolutions

4)  Double Angle Formulas

5)  Half-Angle Formulas (Make sure your formula sheet has these written on there…)

6) Reference Triangle Examples (Older example, but still helpful)


Day 50: February 27th:

Juniors: Good luck on the ACT.  See you Thursday.

Non-Juniors:  Period 1 meets in room S-028.  Period 2 goes to the library.  Period 3 goes to the library.  Here are some review problems:  PC5-ReviewProblems

Day 49:  February 23rd:  Objective:  Students will apply half-angle formulas to evaluate trigonometric expressions.  Previous Homework Solutions:  SkillBuilderKey and PC5-4AKey and PC5-4QuizKey and PC5-MidUnitReviewKey.  Homework:  PC5-5A Off-Topic Link:  Check out this link explaining some concepts visually.

Updates:   Since the snow has caused us to miss a day we will need to adjust our schedule.  Additionally, the ACT on Tuesday February 27th will cause all Juniors to miss class.  This means I’ll only see you once this week (Friday) and once next week (Thursday).  We will take those days to review what we just covered, introduce a new concept (Half-Angle Formulas) and then review for the test the following week.  Looking forward to catching back up!

ACT Practice Test:  ACT Practice Test  The key is on page 58.

Test-Retakes:   Student who have re-taken the last test have grades that are entered into Synergy as of now (2/24/18 – 10:00am).

Day 48:  February 16th.  Objective:  Students will review unit material by completing a mid unit review in groups.  Homework:  On the post from February 14th, I’ve posted the four items that are due next class.

Day 47:  February 14th.  Objective:  Students will use double angle formulas to solve trigonometric expressions and establish identities.  Homework:  You have three things that are assigned for next class, and one will be assigned on Friday (when I’m out).

  1.  Complete the skill builder  PC5-4SkillBuilder
  2. Complete the worksheet PC5-4A  PC5-4A
  3. Complete the take-home quiz. PC5-4Quiz
  4. Complete the review.  PC5-MidUnitReview  (I’ve provided the solutions here:  PC5-MidUnitReviewSolutions)

Day 46:  February 12th.  Objective:  Students will use the sum and difference formulas to evaluate trigonometric expressions.  Homework:  PC5-3A and PC5-3B.  Trig Cheat Sheet:  Trig_Cheat_Sheet_Reduced

Day 45:  February 8th.  Objective:  Students will solve trigonometric equations given an interval.  In-Class Notes:  SolvingTrigEquationsNotes Homework:  Finish the two worksheets from last class.  They can be found in the previous post below 🙂

Day 44: February 6th.  Objective:   Students will solve trigonometric equations given an interval.  Assignments/Homework:  PC5-2A   and  PC5-2B.  Helpful videos:  Solving Trig Equations Part 1  AND Solving Trig Equations Part 2.

Day 43: February 2nd.  Objective:  Students will simplify trigonometric expressions and verify establish identities.  Helpful videos:  Simplifying Trig Expressions AND: Simplifying Homework:  PC5-1Assignment Partial Key:  PC6-1HWScan1     PC6-1HWScan2

Unit 4:  Trigonometry

Day 42: January 31st.  Objective:  Students will prove their knowledge on trigonometric functions by completing an individual test.   Homework:  Previewing the next chapter will require you to take some notes from the textbook.  Starting on page 475 there are various identities.  After taking the time to read through section 6.1 (p475 – 479), copy down the notes for Quotient Identities, Reciprocal Identities, Pythagorean Identities, and Even/Odd Identities.  Next, familiarize yourself with establishing identities by copying and completing examples 1, 2, 3, and 4 starting on page 476.  These are already worked out in the textbook, so copy them but also form some questions about the process for the start of class. Here are the pictures of the book I took:  p475   p476(1)    p476(2)    p477

Day 41: January 24, 25, 26.  Objective:  Students will complete a group test to help review for an individual test.

Day 40: January 22nd. Objective:  Students will review unit material to prepare for a group test.  Review:  PC4-Review Review Key:  PC4-ReviewKey Homework:  Be ready for the group test during finals week.  Also be ready for your individual test on the first day of 2nd semester.

Day 39: January 18th.  Objective:  Students will use the inverse trigonometric functions to find angles. Notes:  PC4-6Notes Classwork Assignment: PC4-6InversePractice Homework:  p. 467 #’s 1-45 odd.

Day 38: January 16th.  Objective:  Students will find the zeros of a trigonometric function using a graph.  Students will write the equations of trigonometric functions given a graph or details about the graph.  Notes: PC4-5NotesKey Homework: p. 450 #’s 1-11 odd, 21-26 all, 31-37 odd (just graph the function and ignore the “steps” it mentions in the description).

Day 37: January 11th. Objective:  Students will graph trigonometric functions.  Notes:  PC4-4Notes and PC4-4Toolkit Homework:  PC4-4

Day 36:  January 9th. Objective:  Students will complete reference triangles given information about an angle or trigonometric function. Notes:  PC4-3Part1Notes and PC4-3Part2Notes Class Assignment:  PC4-3 Homework: p. 429 #’s 1-7 odd, #’s 17, 19, 25, 29.  #’s 33-39 odd.

Day 35: January 5th.  Objective:  Students will complete the unit circle. Unit Circle Video #1: Unit Circle Background Unit Circle Memorizing Method: Unit Circle Values Notes:  IntroTrigNotesPC4-2 Class Assignment:  PC4-2Practice Homework:  p. 417 #’s 1-9 odd, #’s 11, 15, 19, 23, 31, and 33.

Day 34: January 3rd. Objective:  Students will review basic concepts on angle measure and arc length. More Notes: DMSNotes and  Trig-Intro Notes  Skill Builder:  PC4-1Skillbuilder Homework:  p 404 #’s 1-39 odd, 43-67 every other odd, #69 and #75. For a Bonus stamp:  Complete #70, 73, and 77 AND be able to explain and show your work.

12-18-17 Update:  I’m still working on grading your finals.  Will post to synergy when I am finished.

Homework for break:  Check out these notes that go along with your book:  Trig-Intro Notes  You should be looking at your book as well – chapter 5.  I’m also attaching a glue-in from my Geometry class that includes information you absolutely need to know. G4 – SOHCAHTOA Official assignment:  p 404 #’s 1-39 odd, 43-67 every other odd, #69 and #75.  Last year we had many breaks due to snow.  Feel free to check out some links from my precalculus class last year.

Semester 1 Final Exam (December 13th and December 15th):

In order to prepare for the Final Exam, you should:

  1.  Review all daily quizzes from this semester
  2. Review/Re-do each chapter review/group test for the unit tests
  3. Complete the Final Exam Review (Complete problems in your notebook!)
  4. Prepare questions to ask in class

Here is a Final_Exam_Review (Created by a professor at PCC – A. E. Cary)

Here are the Solutions (Created by a professor at PCC – A. E. Cary)

Unit 3:  Exponential and Logarithmic Functions

Day 32 and Day 33: December 5th and December 7th.  Part 1 and Part 2 of the Exam

Day 31: December 1st. Objective:  Students will review unit material by completing a review.  Review:  PC3-Review  Review Key:  PC3-ReviewKey1 Updates:  Your test will be given in two parts, the first of which is on Tuesday.  Part 1 (Tuesday) will be focusing on solving for x using logarithms and Part 2 (Thursday) will be on the application problems.  You’ll receive a formula sheet as well as some guidance as to how to round answers.

Day 30: November 29th.  Objective:  Students will use logarithms to find the decibel levels of a sound and the magnitudes of earthquakes.  Notes:  PC3-6NotesKey Classwork-Stations:  PC3-6ClassworkStations Homework:  p. 386 #’s 1-10 ALL.

Day 29: November 27th.  Objective:  Students will solve application problems involving exponentials and logarithms.  Notes:  PC3-5NotesKey Classwork:  PC3-5KeyBack  and PC3-5KeyFront We completed the problems together in class.  Homework:  Finish the problems from the document (#’s 5-10)  PC3-5Assignment

Day 28:  November 20th.  Objective:  Students will use interest formulas to answer application problems.  Notes:  PC3-4Notes Notes Key: PC3-4NotesKey Classwork:  PC3-4Assignment Homework:  p 357 #’s 1-15 odd, 25-33 odd, #37, and #39.

Day 27:  November 16th:  Objective:  Students will review the assignment from last class working through the homework questions together.  Today’s in class notes:  PC3-3SelectedAnswers  I picked what I thought was the best example of the homework and scanned those problems.  Make sure to e-mail me other questions as they come up.  Homework:  Finish the homework from last class if you didn’t already (it’s listed right below).  Also preview the next lesson by reading pages 350-357.  Take notes by writing down the theorems and formulas you see.  When a formula or theorem is shown, make sure to define any variables that occur in the formula.  For example, the Simple Interest Formula on page 350 defines I=Prt.  You should have a sentence or two about what this formula does, as well as an explanation of what I, P, r, and t all stand for.

Day 26:  November 14th.  Objective:  Students will use properties of logarithms to solve equations.Notes:  PC3-3PartANotesKey  and PC3-3PartBNotesKey Homework:  PC 3-3(part1) worksheet #’s 13, 14, 15, 16, 23, 24, 27, 29, 30, 43, 44.  ALSO:  PC 3-3(part 2) worksheet ALL 8 problems.

Day 25: November 7th.  Objective:  Students will find the domain of a logarithm.  Students will complete application problems with exponential and logarithmic functions.  Notes:  PC3-2Notes Class work: PC3-2Assignment Homework:  p. 330 #’s 37-45 odd, #’s 77-82 ALL.  Preview the properties of logarithms for the next lesson!

Day 24:  November 2nd.  Objective:  Students will graph the exponential and logarithmic functions.  Students will convert between exponential and logarithmic functions.  Notes:  PC3-1Notes:Assignment Notes Key:  PC3-1NotesKey Homework: p 320 #’s 39,40,41, and 61.  p. 330 #’s 1-29 odd.

Unit 2: Polynomial and Rational Functions

Day 23: October 31st. Objective:  Students will prove their knowledge by completing a chapter test. Homework:  Preview the next unit on exponential functions and logarithms.  Answer the question:  What is the circle of logs?

Day 21: October 27th.  Objective:  Students will collaborate in order to complete a group test.  Homework:   Study for the individual test on Tuesday! Helpful Study Resource:  Take a look at all of your quizzes from this unit.  We’ve covered quite a bit.  I’m linking the answer key’s right here: PC2-QuizzesKey Also, there are other review problems in your book at the end of the chapter. Group Test (Blank):  PC2-GroupTestPart1and2

Day 20:  October 25th.  Objective:  Students will write equations of rational functions given a graph.  PC2-6 Homework:  Study for the group test on Friday!

Day 19:  October 23rd.  Objective:  Students will identify horizontal and oblique asymptotes in a rational function.  Notes:  PC2-5Notes  Notes Key:  PC2-5NotesKey Assignment: PC2-5PracticeProblems Homework:  Finish all practice problems (in your notebook).  PC2-5PracticeProblems

Day 18: October 19th.  Objective:  Students will determine the x-intercepts, y-intercept, domain, and vertical asymptotes of a rational function.  Notes:  PC2-4Notes Notes Key:  PC2-4NotesKey Assignment (Homework):  PC2-4Assignment.

Day 17: October 17th.  Objective:  Students will determine the number of positive, negative, and imaginary roots using Descartes Rule of Signs.  Students will use the Rational Zeros Theorem to create a list of potential rational zeros of a function.  Notes:  PC2-3Notes Homework:  p. 263 #’s 1,2,3.  p. 264 #’s 11-15 odd, 41-49 odd.

Day 16:  October 12th.  Objective:  Students will simplify expressions necessary for writing solutions for polynomials.  Peer-Graded Quiz:  PC2-2Quiz Practice Problems:  PC2-SkillBuilding Key:  PC2-SkillbuildingKey Homework:  p 273 #’s 45-53 odd, p. 279 #’s 1-9 odd.  Also, watch these two videos:  Descartes Rule of Signs  and Rational Roots Theorem.  Write down one question for each video.  The questions will be required for a stamp.

Day 15: October 10th.   Objective:  Students will write the equation of a polynomial given its roots.  Students will identify the roots of a polynomial.  Intro Notes:  PC2-2(Pre)Notes Key: PC2-2PreKey “Real” Notes:  PC2-2Notes Key:  PC2-2NotesKey(1) and PC2-2NotesKey(2)  Homework:  PC2-2 (complete them all).

Day 14: October 6th.  Objective:  Students will analyze polynomials including power functions.  Class work:  PC2-0 Notes:  PC2-1 Answer Keys:  PC2-0FrontKey , PC2-0BackKey , PC2-1FrontKey and  PC2-1BackKey  Homework:  p 214 #’s 1-6 ALL.  p 224 #’s 1-19 odd. Interesting Link regarding where you study: Economist

Unit 1:  Functions and Their Graphs

Helpful Link: Khan Academy – Functions (You could easily familiarize yourself with many concepts using Khan Academy)  My Channel for Precalculus

Day 13: October 4th.  Objective:  Students will prove their knowledge by completing a test.  Homework:  none.

Day 12: October 2nd.   Objective:  Students will review the difference quotient, transformations, compositions, and inverses to prepare for a test.  Review:  PC1-Review(2) Homework:  Study for the test on Wednesday! Review ANSWER KEY:  PC1-Review(2)KEY

Day 11: September 28th.  Objective:  Students will find the inverse of functions if they exist.  Notes:  PC1-9Notes Completed Notes:  PC1-9CompletedNotes Homework: p 308 #’s 21-29 odd (Verify they are inverses of each other)  #’s 47-53 odd (Find the inverse) Homework Help:  Here is a scan of finding the inverse step-by-step: InvserseStepbyStep

Day 10:  September 26th.  Objective:  Students will explore compositions of functions algebraically, graphically, and in a table.  Notes:  PC1-8Notes Completed Notes:  PC1-8NotesCompleted Practice Problems:  PC1-8Practice Homework:  p. 170 #’s 1-11 odd.  #’s 31-39 odd.

Day 9: September 22nd.  Objective:  Students will perform transformations of functions including reflections, stretches, and shifts.  Notes:  PC1-7Notes Completed Notes:  PC1-7A Completed and PC1-7B Completed Practice Problems (Homework): PC1-7PracticeProblems Helpful videos are linked below in my previous post.  I did explain it differently in class, but it’s the same concept.  

Day 8:  September 20th.  Objective:  Students will evaluate the difference quotient given a function.  Students will translate functions up,down,left, and right.  Notes and Problems:  PC1-5NotesandProblems Glue In:  PC 1-5 Glue In Complete Glue In:  PC1-5NotesScan Class Assignment:  PC1-6Exploration Homework:  p 150 #’s 81-84 all (Just evaluate the difference quotient for each of them).  p. 162 #’s 1-24 all (Make sure to sketch the graph and write the equation for all of them). Helpful Video #1:  Transformations 1  Helpful Video #2: Transformations 2 Helpful Video #3:  Transformations 3 Helpful Video #4:  Transformations 4

Day 7:  September 18th.  Objective:  Students will prove their knowledge by completing a unit test.

Day 6: September 14th.  Objective:  Students will summarize concepts and review for a chapter test.  Review:  PC1-Review  Review Answer Key: PC1ReviewKey Homework:  Complete the review, check your answers, and study for the test next class.

Day 5:  September 12th.  Objective:  Students will determine if a function is even, odd, or neither both algebraically and graphically.  Glue In Notes:  PC1-4 Notes Completed Glue In Notes:  PC1-4CompleteNotes IN Class Assignment KEY:  PC1-4PracticeProblemsKey  Group Practice Quiz:  PC1-GroupPracticeQuiz   Group Quiz Key:  PC1GroupQuizKey Homework: p. 148 #’s 9-23 odd (Part c only) #’s 41-53 odd (Determine even/odd/neither algebraically).

Day 4:  September 8th.  Objective:  Students will identify intervals for when a function is concave up and concave down.  Students will identify local minima and maxima as well as absolute minimum and maximum.  Notes:   PC1-3Notes  (Completed Notes From Class Homework:  p. 151 #’s 85-88 ALL  #’s 95 – 101 Graph with assistance from a device, find the Intervals Increasing/Decreasing, Local Max/Min, as well as find the intervals the graph is concave up/down.  Also:  #103  (TOTAL PROBLEMS – 13).   Video on Increasing/Decreasing and Concavity: YouTube.  Video on problem #103:   YouTube

Day 3:  September 6th. Objective:  Students will identify intervals for when a function is increasing and decreasing including problems involving piecewise functions.  Notes:  PC1-2Notes Homework:  p. 148 #1-8 all, 9-25 odd NOT (c).

Day 2:  September 1st.  Objective:  Students will find the domain of a function algebraically and graphically.  Students will find the range of a function graphically.  Notes:  PC1-1Notes (updated).  Assignment/Homework:  p. 125 #’s 1-13 odd, #’s 21-63 odd.  Show work (including drawing graphs).  Use these scans to do homework if you don’t have a book yet.  2.1-prob.-set-page-1  and 2.1-prob.-set-page-2.  Helpful Video: Domain and Range (Basic).

Day 1:  August 30th.  Objective:  Students will read syllabus, understand course expectations, and pre-assess unit 1 material.  Syllabus: Syllabus Worksheet/Homework: Day 1 what do you know. Helpful Notes from Class:  PC1-0 Notes Scan Supplemental Links: Is it a function?  or What is a function?