#graphs in precalculus

[itskandykane]

have a math quiz tmrw might cry (or disappear into the woods for an undisclosed amount of time)

funniest part is that math is my favorite subject 🥲

[er-cryptid]

[math-journal2]

Precalc 1 — here — Book Ed2

Main: @sock-to-the-third (18+ blog)

“The place where I eat books” ~ me

. . .

Book Edition 1

Pre-Algebra

Unit 0: Fractions

~

Algebra

Unit 1: Solve for x

Unit 2: Inequality

Unit 3: Exponent

Unit 4: Graphing

Unit 5: System of Operations

~

Algebra 2

Unit 6: Functions

Unit 7: Radicals

Unit 8: Imaginary Numbers [21]

Unit 9: Trinomial

Unit 10: Logs

Unit 11: 1/x

Unit 🍎 : Growth & Decay b^x

Unit 12: (f + g)(x)

Unit 🍑: Parent Functions

~

Precalculus

Unit 13: Inequality

Unit 14: Composite f(x)

Unit 15: Inverse f(x)

Unit 16: Radicals

Unit 17: Parabola

Unit 18: Power of i

Unit 19: Power Function

Unit 20: Dividing Polynomials [50]

Unit 21: Dividing Polynomial Functions

Unit 22: Tough 1/x

Unit 23: Basic 1/x

Unit 24: b^x

Unit 25: Graphing Logs

Unit 26: Circles [70]

Unit 27: Ellipse

Unit 28: Parabola

.

.

Old Book

Algebra

Page 1 / Unit 1

[skipped PEMDAS]

Page 2 / Inequalities

Page 5 / Exponents

—-

Page 6

Page 7

Page 8 / Linear

Page 9

Page 10 / Systems of Equation

Page 11

Page 12

Algebra 2

Page 13 / Functions

Page 14

Page 15 / Radicals

Page 16

Page 17

Page 18

Page 19

Page 20 / Imaginary Numbers

Page 21 **

Page 22

Page 23 / Trinomials

[fraction rules]

Page 24

Page 25

Page 26

Page 27 / Logs

Page 28

Page 29

Page 30

Page 31 / [ 1/x ]

Page 32

Page 33

Page 34 / Parent Functions

Precalc

Page 35 / Inequalites — here

Page 36

Page 37 / Piecewise function

14– Page 38 / Composites

Page 39

15– Page 40 / Inverse Functions

16– Page 41 / Radical Functions

17 —Page 42 / Parabola

Page 43

18– Page 44 / i^#

Page 45 / power function (1/x & x^#)

Page 46

Page 47

Page 48

Page 49

Page 50

Page 51

Page 52

Page 53

Page 54

Page 55

Page 56

Page 57

Unit 24

Page 58

Page 59

Page 60

Page 61

Page 62

Page 63

Page 64 — jk it’s 70 now

[mothric]

You're right that if you did just find the sum of all the little dx bits you would just get x, but if you imagine a graph y=f(x), and you want to find the area underneath that line, you split it into lots of little rectangles of width dx then add them together. It's the sum of every y value along that line multiplied by dx. -Sooty

hello sooty my cool friend sooty

I wish I could nod and say "oh I see!" but alas, the introduction of graphs and the letter y has only deepened my confusion. I think I might sort of understand what I'm meant to be visualizing if I squint really hard? but I haven't been in any sort of math class for 10 years and my exposure to a math class with graphs (precalculus) was even longer ago, so it's not your fault lol. I appreciate the attempt to help!

[song-tam]

i am absolutely one hundred percent going to completely bomb this math test holy shit. i hate you trigonometry i hate you graphing i hate you proofs i hate you precalculus. i dont hate the unit circle though the unit circle has never done anything bad for me

[infinitelytheheartexpands]

since i am at home and have access to my yearbooks, it is now time for the roundup of “some of my favorite quotes from people’s yearbook signatures”, a non-exhaustive list:

2010-11 (3rd grade):

-“have a great summer savvanah”—kid in my class who spelled my name wrong lmao

2011-12 (4th grade):

-“your the most legendary person i have ever met”—one of my besties to this day

2012-13 (5th grade):

-“when the world looks down on you, give them 5 and a half reasons to look up at you. you are brilliant. you are a good person. never lose that. never stop dominating.” —one of the then-high school juniors for some reason (i got signatures and messages from SEVERAL juniors and seniors that year for some reason lmao)

-“too bad”—a kid in my class

*could not find 2013-14 :(*

2014-15 (7th grade):

-“stay cool and rock on with those dance moves and work on skating”—another kid who was in our production of xanadu, where i successfully campaigned with the director to not make everyone rollerskate because some of us (myself included) could not rollerskate

-“the cat whiskers come from within”—a girl in the grade below me with whom i am still buddies

-“you are the smartest person i know and don’t let anyone take that away from you”—my now IRL best friend, the first year after he moved to our school, and this was even though at the time we were in the middle of an INTENSE academic rivalry that put a damper on our friendship for a while

2015-16 (8th grade):

-every single kid who wrote HAGS!!! (have a great summer) because it’s funny <3

-“you have been happy when i have been sad so uh…thanks for always cheering me up with just a smile”—a kid in the grade below me

-“savannah, it is really fun having you in the class and i hope we got the party started for you every english class!”—the same kid who spelled my name wrong in 3rd grade; every day at the start of english class i’d say “let’s get this party started!”

2016-17 (9th grade):

-“…you’ll have to come check in and draw me more memes!”—my 9th grade history teacher, context being that she pitted all the kids in my grade against each other in a year-long history meme war and i, being a dumbass, did not know how to make memes online using generators and shit, so i HAND DREW all of my memes on her board and she would take pictures for my entries (for the record: i did not win)

-“this is a good yearbook. you are a good person. have a good summer.”—one of my guy friends in my class

-“we’re gonna need you in quiz bowl. also how is this handwriting.”—another guy in my class; the reference to the handwriting was because we had to proofread each other’s handwritten essay drafts in english class and i straight up could not read like half of his and he got PISSED as a result

2017-18 (10th grade):

-“dear savannah, have a great summer! read lots of books and eat lots of food because those things make you happy and happiness is great.”—one of my friends in my class, also that is sound advice

-“*sine graph* there, i sined it.”—my precalculus teacher

-“i am ‘cosining’ it.”���the same kid who wrote the handwriting comment the previous year; written directly under the previous signature

-“savannah, mashed potatoes…”—the bestie who wrote the “legendary” comment in 4th grade; the whole message was much longer but we had an inside joke going about how i’m super-picky about my mashed potatoes lol

2018-19 (11th grade):

-“you are just the sweetest little ol’ thang”—one of my friends in my class

-“thanks for making this a great year. you’ve always been so nice to me. never forget that no matter what, you have a good heart, don’t forget that!”—one of the seniors that year; we were in all the musicals and choir together for a few years

-“stay frosty! your joy for life is special, don’t ever let anyone diminish it. change the world.”—a beloved history teacher who moved away after that school year

*no signatures for 2019-20 because COVID :(*

[pepperandeuphoria]

5

Joyce was feeling paranoid in her room, which was on the second story. Her walls were coated with the hottest of pinks and covered in various art pieces which spelled out the way that she felt throughout the years. Mostly paintings of flowers and landscapes, she appreciated the complexity of flowers. As she looked down she saw the work put before her. A study sheet,  for her precalculus final, which was to take place in a couple of days, and beside it, her Adderall. She opened the box of pills and inside there were none. She closed it again. 

She checked the locks on her door and her windows and made sure there was no chance that her isolation could be broken, and then she checked the box again. Still nothing. She got out her phone and began looking at Snapchat, which was her preferred method of getting more pills. She hadn’t had one all day and it was getting a little hard for her to focus. She texted her dealer, Rufio, and waited for a response. While she was waiting she checked the pill box again. Still nothing. 

Rufio responded complaining about the late hour that she was asking him to deliver. He said he would do it, but only if he got a $10 delivery fee in return. Joyce agreed and Rufio was on his way. 

Outside Joyce’s window was a slanted roof which gave way to a sort of pathway that could be taken to the ground. It was a dangerous way to have the house set up when they were kids, but it was very convenient now that she used it to sneak out. She saw Rufio’s car at the gate and unlocked the window. She grabbed $110 and put it in her back pocket, and opened up her window, climbing out and making her way to the ground, where she would begin to run toward Rufio and open the gate. She got in the passenger seat of his car and held the money in her hand. The deal was made and she went back to her room. 

She dumped the bag of pills into her box, took out three, and began crushing them. She didn’t bother to look at the dosage of the pills before beginning her routine. She crushed them up in a dime bag that she’d been using and reusing for 2 years now, which was coated all throughout the inside with a fine particulate that couldn’t be retrieved except with water. She dumped the powder out onto a hand mirror and snorted it using a piece of a plastic straw. 

She began to study with her newfound energy. She was starting to get better at making her graphs, which was good because that’s kind of what calculus is all about. She was finished with the tenth problem when she decided that she’d reward herself with more Adderall.

First / Prev / Next

[tutoringmaphy01]

Navigating AP Precalculus Tutor: Common Student Challenges and Solutions | Tutoring Maphy

Navigating AP Precalculus: Overcoming Common Student Hurdles with Expert Guidance

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[isabelledoesmath]

Why I'm learning Blender

In mathematics, we often work in detail with shapes and lines. We analyze slopes, intercepts, and confined areas in order to create a mathematical picture. Because of this, from the second we start to teach mathematics, we use images and graphs. To show that the sum of two and three is five, we might draw a representation of the numbers as cookies or apples. To show that the slope of a parabola at its vertex is zero, we might plot some points and connect the dots.

As a senior in college studying mathematics, I have found myself drawing countless graphs and diagrams of the shapes and formulas I have been working on. Even when dealing with abstract concepts, I use a combination of colors and points to explain what is happening. When tutoring precalculus, my first method of explaining a concept is always a drawing.

Bettina Rosken and Katrin Rolka did research through the University of Duisburg-Essen, Germany, that shows the importance of visualization in mathematics regarding calculus. They state that “visualization allows for reducing complexity when dealing with a multitude of information,” (Bettina and Rolka 458). Being able to see a graph and label every important point allows students to keep their work clear and concise. The authors, however, make a point that a drawing or representation of the mathematical concept only does so much; a mathematical model cannot stand by itself without an understanding of what it is and its rules.

While math is best learned in a classroom, Blender, a 3D modeling program, can be one of those tools that can help assist in understanding concepts outside of class time. As much time as I can spend on drawing a graph of a 3D shape like a donut, more commonly known in the math world as a torus, if I can instead learn a program that allows me to hold two keys down and click through some interface to place a torus into a world, then I can push my understanding of mathematics even further in less time.

And that is what I have done. So far, I have spent time learning how to place shapes, edit the world around them, and their materials. While I will not need to necessarily be able to create a sphere that is reflective in order to understand a math problem, the more I understand the entire interface and abilities of Blender, the better I will be able to use it. Understanding both what to use and what not to will allow me in the future to focus further on the mathematical side of this program and how I could have used it in the courses I have taken. This week, the final project I made was a lighthouse on a rock with some small houses around it. I learned how to sculpt different shapes, create different light sources, and assign different colors to different faces. All of this was thanks to Grant Abbitt’s course on Udemy with GameDev, titled Complete Blender Creator: Learn 3D Modeling for Beginners.

Rösken, Bettina, and Katrin Rolka. "A picture is worth a 1000 words–the role of visualization in mathematics learning." Proceedings 30th conference of the International Group for the Psychology of mathematics education. Vol. 4. Prague: Charles University, 2006.

[tutoringmaphy]

AP Precalculus MCQ #3 Which of the following functions has a zero at x=3 and has a graph in the

[lvrstudy]

today is the day that all my school grades have been released, so i only have to wait until july for my report card. i went to debate camp and i made friendship bracelets, something i haven't done for three years. for my second precalculus class, i did my readings, which are about graphing trig and inverse trig functions. i also made myself a chocolate chip mug cake <3

[er-cryptid]

[educationistop]

is a survey of calculus hard

Survey calculus is one of the easiest calculus subjects students can take, it is made for students who are majoring in branches like economics, business, psychology, social science, etc. In other words meaning the majors that don’t focus a lot on math, not like engineering, mathematics, or physics.

These are the 7 main topics that students take and Survey car colors:

Precalculus review

Functions and graphs

Limits and continuity. 

Introduction to differentiation and basic rules for differentiation.Implicit differentiation and related rates. 

Use of derivatives to study absolute maxima/minima and to sketch graphs of functions.

The constant e and continuously compounded interest. 

Integration: indefinite integrals and anti-differentiation, definite integrals, and the Fundamental Theorem of Calculus determining area between curves, integration by parts.

So, General business majors are advised to take read more...

[math-journal2]

Book Ed1 - here — Precal 2

Book Ed2

By @sock-to-the-third (18+ blog)

Parabolas

Inequality

Exponents

.

Unit 0: Pre-Algebra

.

Algebra

Unit 1: Solve for x

Unit 2: Inequality

Unit 3: Exponent

Unit 4: Graphing

Unit 5: System of Operations

~

Algebra 2

Unit 6: Functions

Unit 7: Radicals

Unit 8: Imaginary Numbers [21]

Unit 9: Trinomial

Unit 10: Logs

Unit 11: 1/x

Unit 🍎 : Growth & Decay b^x

Unit 12: (f + g)(x)

Unit 🍑: Parent Functions

~

Precalculus

Unit 13: Inequality

Unit 14: Composite f(x)

Unit 15: Inverse f(x)

Unit 16: Radicals

Unit 17: Parabola

Unit 18: Power of i

Unit 19: Power Function

Unit 20: Dividing Polynomials [50]

Unit 21: Dividing Polynomial Functions

Unit 22: Tough 1/x

Unit 23: Basic 1/x

Unit 24: b^x

Unit 25: Graphing Logs

Unit 26: Circles [70]

Unit 27: Ellipse

Unit 28: Parabola

— hyperbola

[textileebook]

Precalculus with Limits, 5th Edition PDF by Ron Larson

Precalculus with Limits, Fifth Edition By Ron Larson Contents: 1. Functions and Their Graphs 1 1.1 Rectangular Coordinates 2 1.2 Graphs of Equations 11 1.3 Linear Equations in Two Variables 22 1.4 Functions 35 1.5 Analyzing Graphs of Functions 49 1.6 A Library of Parent Functions 60 1.7 Transformations of Functions 67 1.8 Combinations of Functions: Composite Functions 76 1.9 Inverse Functions…

[mathsprogram]

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