Algebra and Trigonometry: Functions
4.0 (2 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
703 students enrolled
Wishlisted Wishlist

Please confirm that you want to add Algebra and Trigonometry: Functions to your Wishlist.

Add to Wishlist

Algebra and Trigonometry: Functions

Learn the Important Underlying Concept of Functions in Mathematics
4.0 (2 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
703 students enrolled
Created by Great IT Courses
Last updated 6/2017
English
Current price: $10 Original price: $120 Discount: 92% off
5 hours left at this price!
30-Day Money-Back Guarantee
Includes:
  • 22.5 hours on-demand video
  • 1 Article
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I Learn?
  • Have a strong foundation and understanding of functions
  • Have a strong foundation of the underlying concepts of calculus
View Curriculum
Requirements
  • High School Basic Algebra
Description

This course teaches you all the important underlying concepts in functions in Mathematics. The knowledge that you gain here can be further completed in our next courses towards a complete mastery of calculus. 

This course covers the following topics: 

  • Function and Function Notation
  • Domain and Range of Functions
  • Rates of Change and Behavior of Graphs
  • Composition of Functions
  • Transformation of Functions
  • Absolute Value Functions
  • Inverse Functions

As described above, this course can also be taken in combination with our other courses in this course series. If you're interested in learning mathematics with us all the way up to calculus, please read our "Mathematics" page on "Greatitcourses" website. 

Who is the target audience?
  • This course is for you if you're planning a career in Engineering, Programming, Science, etc. where you'd need a strong foundation in mathematics.
  • This course is also for you if you're changing careers and need to use the discussed concepts in your future career, for example as a computer programmer.
Students Who Viewed This Course Also Viewed
Curriculum For This Course
130 Lectures
22:33:02
+
3.0 - Introduction
6 Lectures 23:01



How to Best Use This Course
05:14

Feedback
04:36

Legal Disclaimer
00:06
+
3.1 - Functions and Function Notation
18 Lectures 03:56:53
Here we’ll have a short discussion about the topics covered in this course, how to get a copy of the textbook if you had any problems finding that and the section in the book we’re covering in this course. We’ll also show you where this course is on the main road map on greatitcourses.com.
Preview 06:29

Here, we’ll have a discussion and a general overview of the concept of functions to build a foundation upon which we can build the rest of the course.

Preview 17:40

Here, we’ll have a discussion and a general overview of the concept of functions to build a foundation upon which we can build the rest of the course.

Preview 19:34

Here, we’ll have a typical coffee shop menu and based on that decide whether price is a function of item and vice versa.

Preview 10:54

Here, we’ll solve two examples, first a typical average grade system and second a list of famous baseball players of all time. In each case, we decide whether one set can be considered a function of the other one and vice versa.

How to Determine If a Relation a Function - Exercise
10:18

In this video, we’ll talk about function notation like f(x). We learn how and in what situations we can use that and what is basically represented by it. Moreover, we’ll do some examples to learn the concept better.

Function Notation
19:41

In this video, we’ll study some relationships between pairs of numbers represented in form of tables. Each table has a set of inputs and outputs. After studying each table, we decide whether the table represents a function or not.

Representing Functions Using Tables
10:00

In this video, you’ll learn how to evaluate functions at different points for inputs. We’ll also learn what the inverse of this situation would look like. Moreover, we’ll go through some example to solidify the concepts learned here.

Finding Input and Output Values of a Function
15:58

In this video, you’ll learn how to figure out the input values in a function that created a specific output.

Evaluating Functions - Exercise
12:29

In this video, you’ll learn how to determine whether a variable in a formula is a function of the other variable. For example, in the formula x² + y² = 1, you can determine whether y is a function of x or not.

Evaluating a Function Expressed in Formulas
15:38

In this video, you’ll learn how to evaluate function values by reading the information related to the function represented in a tabular form. Each input in the table corresponds to an output and so based on that, you can evaluate any desired input.

Evaluating a Function Given in Tabular Form
09:15

In this video, you’ll learn how to use the graph of a function in order to determine the output value related to any input value present in the domain of the function. For example, by looking at the graph of a function, you can identify which output is related to the input x =4 and based on that you can write, f(4) = “that identified output value read on the graph”. You can also do this to solve equations like f(x) = 2, in which you could identify for which value/values of x, you would have an output value of 2.

Finding Function Values from a Graph
08:23

In this video, you’ll learn how to determine whether a function is one-to-one, meaning that each output value corresponds exactly to one input value and that there are no repeated x or y values. We’ll also do some exercises to understand the concept better.

Determining Whether a Function is One-to-One
17:49

In this video, you’ll learn how you can use a vertical line, run it through the domain of a function parallel to the y axis to decide whether a graph represent a function or not.

Vertical Line Test
11:12

In this video, you’ll learn how you can use a horizontal line, run it through the range of a function, parallel to the x axis, to decide whether a function is one-to-one or not.

Horizontal Line Test
14:29

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

Basic Toolkit Functions (Part 1 of 3)
17:36

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

Basic Toolkit Functions (Part 2 of 3)
14:00

In this video, we’ll graph some toolkit functions like f(x) = x². These are the kind of functions that are used very often in mathematics. We’ll also talk about some important characteristics of them, like vertex, minimum, maximum, domain and range.

Basic Toolkit Functions (Part 3 of 3)
05:28
+
3.2 - Domain and Range
12 Lectures 02:42:11
Domain and Range Introduction
12:23

In this video, we’ll give you a summery of the interval notation. For example, x > a on a number line in interval notation as (a, infinity). We’ll also do a few examples finding the domains of a few functions.

Interval Notation Summery
15:30

In this video, you’ll learn how to find the domain of a function. We’ll also do a few exercises to learn the concept properly.

Finding the Domain of a Function - Exercise
15:26

In this video, you’ll learn how to find the domain of a function. We’ll also do a few exercises to learn the concept properly.

Finding the Domain of a Function - Exercise
16:14

In this video, you’ll learn how to use inequality notation, set-builder notation and the interval notation to specify domain and range of a function.

Inequality, Set-builder and Interval Notations
13:03

In this video, you’ll learn how to describe sets on a real-number line in set-builder, inequality and interval notations.

Describing Set on the Real-Number Line
08:37

In this video, you’ll learn how to find the domain and range of functions based on the graph of the function. We’ll also do some examples to learn the concept better.

Finding Domain and Range From Graphs
19:01

In this video, we’ll study the domains and ranges of some famous toolkit functions.

Finding Domains and Ranges of the Toolkit Functions
19:17

In this video, we’ll find the domain and range of square root functions.

Finding the Domain and Range of Functions - Exercise
06:43

In this video, you’ll learn what piecewise-defined functions are and in what sort of situations they can be used.

Piecewise-Defined Functions
16:06

p190, e12 - In this video, you’ll learn how to interpret and graph a piecewise function that represents how a cell phone company charges their customers for data transfer.

Working with a Piecewise Function - Exercise
10:34

p191, e13 - In this video, we’ll draw the graph of a piecewise functions that consists of a three pieces.

Graphing a Piecewise Function - Exercise
09:17
+
3.3 - Rates of Change and Behavior of Graphs
14 Lectures 02:12:16

In this video, we’ll introduce the concept of rate of change. We’ll use an example of the average cost of a gallon of gasoline in dollars over the period of 7 years from 2005 to 2012 and study the change in cost over different periods between the two years.

Rate of Change Introduction
13:11

In this video, we'll learn the practical meaning of average rate of change using a practical example.

Rate of Change Formula and Example
09:03

Computing an Average Rate of Change based on a Table
14:15

Computing an Average Rate of Change based on a Function Graph
12:26

Computing an Average Rate of Change based on a Function Formula
10:48

In this video, we'll go through two interesting examples of calculating the average rate of change.

Computing an Average Rate of Change - Example
12:40

Increasing, Decreasing, Local Minimum, Maximum, Extrema - Part 1
14:57

Increasing, Decreasing, Local Minimum, Maximum, Extrema - Part 2
03:56

In this video, we're going to analyze the graph of a function and identify in what intervals the function is increasing or decreasing.

Finding Increasing and Decreasing Intervals on a Graph
06:23

Finding Extrema of a Function using Technology
11:36

Finding the Local Maximum and Local Minimum of a Function - Example
01:56

Analyzing the Toolkit Functions for Increasing and Decreasing Intervals
09:34

Absolute Minimum and Absolute Maximum of a Function
06:37

Finding the Absolute Minima and Maxima of a Function - Example
04:54
+
3.4 - Composition of Functions
14 Lectures 02:07:57
Composition of Functions - Concept
14:24

Combining Functions Using Algebraic Operations
12:55

Combining Functions Using Algebraic Operations - Example
07:40

Composition of Functions - Concept and Mathematical Notation
12:36

Composition of Functions Not Commutative - Exercise
04:39

Composition of Functions - Exercise
04:16

Composition of Functions - Exercise
07:06

Evaluating Composite Functions Using Tables
05:59

Evaluating Composite Functions Using Graphs
06:31

Evaluating Composite Functions Using Function Formulas
10:07

Finding the Domain of a Composite Function - Part 1
14:12

Finding the Domain of a Composite Function - Part 2
09:49

Finding the Domain of a Composite Function - Exercise
08:20

Decomposing Composite Functions
09:23
+
3.5 - Transformation of Functions
40 Lectures 06:52:24
Transformation of Functions - Introduction
13:08

Vertical Transformation of Functions
11:51

Vertical Shift - Example
05:24

Vertical Shift - Example
07:19

Horizontal Shift of Functions
14:19

Horizontal Shift to Right and Left - Part 1
14:30

Horizontal Shift to Right and Left - Part 2
05:30

Horizontal Shift - Example
07:53

Inside and Outside Changes Affecting Domain or Range
06:34

Shifting a Tabular Function Horizontally
05:57

Identifying a Horizontal Shift of a Toolkit Function
08:06

Horizontal Function shift - Example
06:40

Graphing Combined Vertical and Horizontal Shifts - Example
11:03

Identifying Combined Horizontal and Vertical Shifts - Example
10:44

In this video, we're moving the toolkit reciprocal function to the right and up. We'll then find the formula of the transformed function, draw the graph of both functions and compare them.

Transformation of Functions - Example
06:46

Reflecting Function About the x and y axes - Introduction
11:07

Reflecting a Graph Horizontally and Vertically - Example
10:43

Reflecting a Graph Horizontally and Vertically - Example
10:58

Reflecting a Tabular Function Horizontally and Vertically - Example
04:59

In this video, we're developing a function that represents a learning model. The function is a transformation of one of the toolkit functions. Three steps of transformation are applied to the function. 

Applying a Learning Model Equation - Example
13:11

In this video, we're going to graph the vertical and horizontal transformations of the toolkit function f(x) = x^2

Graphing the Vertical and Horizontal Transformations of a Toolkit Function
06:44

Even and Odd Functions - Part 1
14:46

Even and Odd Functions - Part 2
08:26

In this video, we have a function in the form of a polynomial of degree 4. We'll verify whether the polynomial is even or odd. 

Even and Odd Functions - Example
08:38

Vertical and Horizontal Compression and Stretches - Part 1
09:59

Vertical and Horizontal Compression and Stretches - Part 2
13:38

Vertical and Horizontal Compression and Stretches - Part 3
13:27

p234

Vertical Stretch of Functions and Example
12:37

p236

Finding a Vertical Compression of a Tabular Function
07:33

p236

Recognizing a Vertical Stretch - Example
07:52

p237 - In this video, we're taking the identity toolkit function, f(x) = x and stretch the function and move it down as well. We'll create a formula for the new function and draw the graph as well. 

Function Formula Transformation - Example
07:30

p237

Horizontal Compression and Stretches - Concept
14:47

p238 - In this video, we'll create a new function based on a population of fruit flies. The new function created based on the original function progresses through its life span twice as fast as the original function and so it represents a horizontal compression. 

Graphing a Horizontal Compression - Example
14:41

p238 - In this video, we'll create a new function based on a population of fruit flies. The new function created based on the original function progresses through its life span twice as fast as the original function and so it represents a horizontal compression. This is the same problem as the last video. It has been solved in a different way. 

Graphing a Horizontal Compression - Example
14:06

p238, e17 

Finding a Horizontal Stretch for a Tabular Function
12:44

p239, e18

Recognizing a Horizontal Compression on a Graph
06:19

p239, ti11 - In this video, we take the toolkit square root function and stretch it by a factor of 3. We then find the formula of the stretched function. 

Finding the Formula for a Stretched Toolkit Function
14:00

p240

Performing a Sequence of Transformations
13:29

p240, e19 

Finding a Triple Transformation of a Tabular Function - Example
09:30

p241, e20

Finding a Triple Transformation of a Graph
14:56
+
3.6 - Absolute Value Functions
7 Lectures 01:07:10

p247

Absolute Value Function - Introduction
14:20

p247

Absolute Value - Example
03:54

p248

Graphing an Absolute Value Function
09:42

p248, e2

Writing an Equation for an Absolute Value Function Given a Graph
11:44

p249, ti2

Absolute Value Function Transformation - Example
07:06

p251, e3

Finding the Zeros of an Absolute Value Function - Example
12:25

p251, ti3

Solving an Absolute Value Equation
07:59
+
3.7 - Inverse Functions
19 Lectures 03:11:10

p254

Inverse Functions - Introduction
13:59

Domain, Codomain, Range and Image of a Function
11:36

One-to-one or Injective Functions
05:35

Onto or Surjective Functions
08:15

Bijective or One-to-one Correspondence Functions
13:16

p256, e1

Identifying an Inverse Function for a Given Input-Output Pair - Example
10:00

p256, ti1

Original and Inverse Functions Input-Output Pairs
01:39

p256, e2

Testing Inverse Relationships Algebraically - Example
07:12

p257

Finding the Domain and Range of Inverse Functions
13:31

p258, e4

Finding the Inverse of Toolkit Functions - Part 1
13:49

p258, e4

Finding the Inverse of Toolkit Functions - Part 2
11:08

p259

Inverting Tabular Functions
05:25

p260, e6

Evaluating a Function and its Inverse from a Graph at Specific Points
07:54

p260

Finding Inverses of Functions Represented by Formulas - Part 1
13:14

Finding Inverses of Functions Represented by Formulas - Part 2
13:51

p260, e7

Inverting the Fahrenheit-to-Celsius Function - Example
07:40

p261, e8

Solving to Find an Inverse Function
11:31

p261, e9

Solving to Find an Inverse with Radicals
11:49

p262, e10

Finding the Inverse of a Function Using Reflection about the Identity Line
09:46
About the Instructor
Great IT Courses
4.2 Average rating
118 Reviews
5,955 Students
8 Courses
Web Development Learning Solutions

At Great IT Courses, you Learn Web Development From Scratch. We have Found the Perfect Way of Teaching IT Skills that you Can Instantly Use in Your Web Development Career Instantly. We Are Very excited to Share it With You!

With us, you start with simple HTML and CSS. We'll take you all the way through server-side programming and scripting. We are confident that you'll love our courses because we do!