Embedded Files
Lecture & Guided Notes:
Lecture & Guided Notes:
The instructor has typed up guided notes for each chapter for the course. These guided notes are distributed in class.
LECTURE NOTES ARE NOT TO BE TURNED IN. Keep them in a safe place, and use them during homework and quizzes.
Remember: As you take a quiz or exam, please bear in mind that answers must be verified using methods studied in this course – your work must be consistent with the methods from the notes.
Homework:
Homework:
After we have completed a lecture section in class, please work on your textbook homework.
The list of homework problems assigned are listed below.
Note: The symbol § means "section", e.g. § 1.1 means "Section 1.1".HOMEWORK IS NOT TO BE TURNED IN. Keep it in a safe place, and use it during quizzes and to prepare for your exams.
Chapter 1 - Functions, Graphs, and Models
Chapter 1 - Functions, Graphs, and Models
🟩 Start of Exam 1 Material
🟩 Start of Exam 1 Material
Section 1.2: Functions
Section 1.2: Functions
READ Section 1.2 from your textbook, and then work on the homework assignment
§ 1.2 TEXTBOOK HOMEWORK: #'s 11 - 21 odd, 29 - 33 odd, 37, 39, 41 - 47 odd*, 51, 79
Chapter 1, Section 2: Homework Updates
Chapter 1, Section 2: Homework Updates
Hi class!
Sometimes the homework textbook directions are a little weird. Please see below for a clarification and/or update to the directions assigned for homework.
The directions for the exercises in the #'s 41 - 55 block read:
"Find the domain of the indicated function. Express answers informally using inequalities, then formally using interval notation".
PLEASE REVISE THESE DIRECTIONS TO:
"Find the domain of the indicated function. Express the domain in interval notation".
Missed something from class or simply miss the teacher's voice? Then feel free to review any or all of the following videos (OPTIONAL).
Note: In the videos you may find extra or different practice problems than those done in class. Feel free to also review these additional problems.
⏸︎ Oh, and please pause and rewind the video as often as you'd like ⏪︎
Lecture and video solutions for Section 1.2
Identify functions.
Find domain and range
Vertical Line Test
Example:
Function notation
Evaluate functions
Difference Quotient
Review on interval notation
Find the domain of polynomial functions, rational functions, and radical functions.
Section 1.4: Functions - Graphs and Transformations
Section 1.4: Functions - Graphs and Transformations
READ Section 1.4 from your textbook, and then work on the homework assignment
§ 1.4 TEXTBOOK HOMEWORK: #'s 5 – 15 odd, 21 – 33 odd, 37, 39, 47 – 59 odd
Missed something from class or simply miss the teacher's voice? Then feel free to review any or all of the following videos (OPTIONAL).
Note: In the videos you may find extra or different practice problems than those done in class. Feel free to also review these additional problems.
⏸︎ Oh, and please pause and rewind the video as often as you'd like ⏪︎
Determine whether the function is even, odd, or neither.
Introduce the parent graphs of six basic functions
Use Desmos to introduce transformation of the graph
Introduce horizontal shifts
Introduce vertical shifts
Without a calculator, apply a transformation of the graph to one of the six basic functions.
Apply horizontal shifts
Apply vertical shifts
Introduce vertical stretch or shrink
Introduce horizontal stretch or shrink
Example:
Without a calculator, apply a transformation of the graph to one of the six basic functions.
Introduce how to reflect a graph about the x-axis or y-axis.
Without a calculator, apply a transformation of the graph to one of the six basic functions.
Indicate how a graph relates to the graph of a basic function
Write the equation of a given graph
Given a non-basic function, apply transformations of the graph
Section 1.3: Functions – Graphs and Properties
Section 1.3: Functions – Graphs and Properties
READ Section 1.3 from your textbook, and then work on the homework assignment
§ 1.3 TEXTBOOK HOMEWORK: #'s 7 (omit part h), 9 (omit part h), 11 (omit part h), 13 - 21 odd, 25 - 29 odd, 41 - 47 odd, 91, 93*
*Stuck on #93? If so, then go to your textbook's Section 1.1, and read Example 6.
Missed something from class or simply miss the teacher's voice? Then feel free to review any or all of the following videos (OPTIONAL).
Note: In the videos you may find extra or different practice problems than those done in class. Feel free to also review these additional problems.
⏸︎ Oh, and please pause and rewind the video as often as you'd like ⏪︎
Video 1:
Given the graph of a function, identify the intervals where the function is increasing, decreasing, or constant.
Video 2:
Given the graph of a function, find
local max
local min
intervals where the function is increasing, decreasing, or constant
Video 3:
Use a graphing calculator to find the local max, local min, and intervals where the function is increasing, decreasing, or constant.
Video 4:
Use a graphing calculator to find the x-intercepts, y-intercepts, local max, and local min.
Video 5:
Use a graphing calculator to find the maximum profit.
Video 6:
Create a cardboard box with no top from a flat sheet of cardboard.
Video 7:
Graphing a piecewise-defined function.
Video 8:
Graphing a piecewise-defined function.
Section 1.5: Operations on Functions; Composition
Section 1.5: Operations on Functions; Composition
READ Section 1.5 from your textbook, and then work on the homework assignment
§ 1.5 TEXTBOOK HOMEWORK: #'s 11 – 27 odd, 31, 39, 43, 45
Missed something from class or simply miss the teacher's voice? Then feel free to review any or all of the following videos (OPTIONAL).
Note: In the videos you may find extra or different practice problems than those done in class. Feel free to also review these additional problems.
⏸︎ Oh, and please pause and rewind the video as often as you'd like ⏪︎
Video 1: Operations on Functions
How to add and multiply functions, and then indicate their domains, e.g.
Find (f + g)(x)
Find (fg)(x)
Video 2: Operations on Functions
How to subtract and divide functions, and then indicate their domains, e.g.
Find (f - g)(x)
Find (f ÷ g)(x)
Video 3: Operations on Functions
Find the sum, difference, product, and quotient of functions by using their graphs
Video 4: Introduce function composition, (f ◦ g)(x)
Find (f ◦ g)(x) and (g ◦ f)(x)
Video 5:
Find (f ◦ g)(x) and (g ◦ f)(x)
Video 6:
Evaluate the composite function, e.g. Find (f ◦ g)(9)
📣 Midterm 1 announcement 📢
📣 Midterm 1 announcement 📢
Midterm 1 Exam will cover Chapter 1 and Chapter 2 (Section 2.1 - 2.3 only).
The midterm will be given after we have finished the corresponding lecture material. The date of the exam will be announced in class.
Section 1.6: Inverse Functions
Section 1.6: Inverse Functions
READ Section 1.6 from your textbook, and then work on the homework assignment
§ 1.6 TEXTBOOK HOMEWORK: #'s 1, 3, 7 – 17 odd, 37 – 47 odd, 57 - 61 odd, 67 -75 odd, 83
Missed something from class or simply miss the teacher's voice? Then feel free to review any or all of the following videos (OPTIONAL).
Note: In the videos you may find extra or different practice problems than those done in class. Feel free to also review these additional problems.
⏸︎ Oh, and please pause and rewind the video as often as you'd like ⏪︎
Video 1:
Identify a one-to-one function.
Use the Horizontal Line Test to determine if a function is a one-to-one function.
Video 2
Use function composition to determine if two functions are inverses of one another.
Video 3
Use the graph of a one-to-one function f to sketch the graph of its inverse. Then find the domain and range of the inverse.
Video 4:
Find the equation of the inverse of a one-to-one function f(x).
Video 5:
Find the equation of the inverse of a one-to-one function f(x).
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