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Lecture Comments (2)

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Post by Baljot Singh on November 22, 2013

In F(X)=x2-x, Why does (x-3)2 later equal X2-6X+9?

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Post by Baljot Singh on November 22, 2013

In F(X)=x2-x, Why does (x-3)2 later equal X2-6X+9?

Function Evaluation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • The Basics: Function Evaluation 0:10
    • Function Definition and Notation
    • Function Evaluation Examples
  • Function Evaluation Mistakes to Avoid 8:47
  • Evaluation of Multiple Functions 9:20

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Charlotte Vilkus

Charlotte Vilkus

Function Evaluation

Slide Duration:

Table of Contents

Section 1: Basic Math
Signed Numbers

18m 58s

Intro
0:00
The Basics: Signed Numbers
0:13
How to Think of Negative Numbers
0:39
Signed Numbers on the Number Line
2:16
Signed Numbers: Addition and Subtraction
3:07
Subtracting a Negative
8:35
The Loss of a Negative is the Addition of a Positive
8:43
Flip the sign!
11:16
Addition and Subtraction Examples
12:19
Signed Numbers: Multiplication and Division
13:45
Quick Rules
15:08
Multiplication and Division Examples
17:02
Section 1: Basic Algebra
Exponents and Roots

24m 44s

Intro
0:00
The Basics: Exponents
0:09
Base and Exponent
0:42
Squared Terms
1:23
Cubed Terms
2:26
Exponent Rules
3:40
Multiplying Terms with the Same Base
5:51
Dividing Terms with the Same Base
6:48
Exponent Term Raised to a Power
8:32
Product of Different Bases to the Same Power
10:14
Quotient of Different Bases to the Same Power
11:57
The Basics: Radicals
17:24
Square Roots
19:39
Divisibility

16m 45s

Intro
0:00
The Basics: Divisibility
0:12
Divisibility Tricks
3:07
The Rules
3:44
Examples of Quickly Determing what a Number is Divisibly by
9:44
Prime Factorization

10m 1s

Intro
0:00
Prime Numbers and Prime Factorization
0:22
How to: Prime Factorization
2:27
Bigger Divisors
5:10
Finding all Factors of 28 and 210
5:52
Powers of 10

8m 56s

Intro
0:00
The Basics: Powers of 10
0:15
Multiplying and Dividing by Powers of 10
2:59
Dealing with Multiplication
3:37
Dealing with Division
5:16
Example Set
6:05
Fractions

12m 50s

Intro
0:00
The Basics: Fractions
0:09
Fractions as Part of a Whole
0:46
Equivalent Fractions
1:10
Fractions: Addition and Subtraction
4:11
Finding the Common Denominator
5:25
Fractions: Multiplication and Division
7:27
Division: Multiplying the Reciprocal (Flip It)
8:53
Fractions: Comparing Fractions
10:36
Determining the relationship between fractions
11:54
Algebraic Expression

17m 39s

Intro
0:00
The Basics: Algebraic Expressions
0:11
Algebraic Expression Definitions
1:54
Simplifying Algebraic Expressions
5:12
Identifying Like Terms
5:23
Using Coefficients to Add and Subtract Like Terms
6:14
Combining Like Terms
8:00
Multiplication of Algebraic Expressions
9:24
Multiplying Two Terms: Coefficients and Variables
9:38
Combining Like Variables in Multiplication
10:15
Multiplying Expressions by a Term
12:08
Example 1: Multiplying Out and Simplifying
13:45
Example 2: Multiplying Out and Simplifying
15:18
Equations

6m 7s

Intro
0:00
The Basics: Equations
0:10
Valid Operations on an Equation
0:26
Isolate the Variable
3:24
Function Evaluation

10m 50s

Intro
0:00
The Basics: Function Evaluation
0:10
Function Definition and Notation
2:23
Function Evaluation Examples
4:55
Function Evaluation Mistakes to Avoid
8:47
Evaluation of Multiple Functions
9:20
Section 2: Geometric Concepts
Geometric Terms and Notation

8m 36s

Intro
0:00
The Basics: Geometric Terms and Notation
0:15
Geometric Notation
6:01
Angles

18m 46s

Intro
0:00
The Basics: Angles
0:09
Classifying Angles
1:40
Acute Angles
1:55
Right Angles
2:21
Obtuse Angles
2:54
Straight Angles
3:46
Angle Relationships
4:13
Complementary Angles
4:28
Supplementary Angles
5:25
Bisected Angles
6:20
Angles at Intersections
7:14
Parallel Lines and Angles
9:50
Drawing Two Intersections to Determine Equal Angles
10:31
Angle Rules
11:20
Shapes and Angles
14:48
Angles in a Triangle
15:23
Angles in a Quadrilateral
15:40
Determining the Number of Angles is Larger Shapes
16:58
Triangles

21m 25s

Intro
0:00
Triangle Basics
0:12
Special Triangles: Isosceles and Equilateral
5:29
Special Triangles: Right Triangles
11:33
Special Triangles: 45, 45, 90 Triangles
18:49
Circles

16m 34s

Intro
0:00
The Basics: Parts of the Circle
0:11
The Diameter
1:04
The Radius
2:08
Arcs and Sectors
3:41
Arc
3:47
Sector
6:41
Using Fractional Weights
7:32
Tangent and Concentric
8:39
Lines that are Tangent to Circles
8:47
Tangent Circles
10:02
Concentric Circles
11:02
Angles in a Circle
11:55
Half Circles and Quarter Circles
12:19
Proportional Areas and Circumferences for Circle Parts
13:29
Inscribed angles
14:37
Volume and Surface Area

10m 53s

Intro
0:00
The Basics: Volume
0:17
Volume Equations
1:52
Equation for the Volume of a Cube
2:30
Equation for the Volume of a Cylinder
3:26
Finding other Volumes
4:14
The Basics: Surface Area
5:26
Surface Area of a Cube
6:30
Surface Area of a Cylinder
8:15
Section 3: Advanced Algebra
Foil

11m 2s

Intro
0:00
The Basics: Foil
0:16
Foil Examples
2:34
Skip Foil: Memorize These
6:22
Factoring

28m 35s

Intro
0:00
The Basics: Factoring
0:12
Factoring: Pull out the GCF
1:07
Example of Pulling Out the Greatest Common Factor
3:41
Factoring: Difference of Squares
5:30
Examples with Difference of Squares Factorizations
6:16
Factoring: General Quadratic Equations
9:35
Zooming in on C
10:12
Factoring Given Quadratic Equations
12:30
Factoring: Special Quadratic Expressions
17:39
How to Decide if You Need a + or -
19:37
Using Factoring in Rational Expressions
21:43
Steps: Take out the GCF, Factor, and Cancel
22:15
Factoring in Rational Expressions: Examples
23:48
Systems of Equations

28m 57s

Intro
0:00
The Basics: Systems of Equations
0:19
Equations with Infinite Solutions
0:44
Number of Equations Should Match the Number of Unknowns
2:41
Why Manipulation and Combination is Often the Best Method
4:34
Why Addition and Subtraction of Equations is Valid
7:23
The Most Important Step--The Common Coefficient
10:41
Manipulation and Combination: Steps
13:50
Substitution
15:49
Which Method Should Be Used?
20:13
How to Solve Problems with Three Equations and Three Unkowns
22:58
Three Equation Example
24:22
Distance Between Two Points

11m 55s

Intro
0:00
The Basics: Finding the Distance
0:13
Breaking Apart X and Y Cooridinates
0:48
Using Pythagorean Theorom
2:53
The Distance Formula
4:26
Example 1: Plugging into the Formula
6:18
Example 2: Using the Given Length to Find a Missing Coordinate
8:20
Intercepts

6m 32s

Intro
0:00
The Basics: Intercepts
0:11
The x-intercept
0:43
The y-intercept
1:44
Determing the Intercepts
3:05
The Special Case: b
4:37
Section 4: Statistics
Average

13m 28s

Intro
0:00
The Basics: Averages
0:11
Finding the Average
2:26
Rearraning the Average Equation
2:59
Average Examples
3:48
Finding the Missing Value
4:32
The Basics: Weighted Averages
6:25
Fractional Weight Method
6:54
Sum and Retake Method
7:48
Weighted Average Examples
8:30
Example Using the Sum and Retake Method
10:50
Median, Mode and Range

10m 8s

Intro
0:00
The Basics: Median
0:23
How to Find the Median
1:01
Quick Median Examples
1:23
The Basics: Mode
5:10
How to Find the Mode
5:16
Quick Mode Examples
5:28
The Basics: Range
7:20
How to Find the Range
8:06
Quick Range Example
8:28
Section 5: The Rest
Rates

17m 49s

Intro
0:00
The Basics: Rates
0:11
Using Units in Rate Problems
1:18
The Classic Rate Problems, d=rt
2:13
Dealing with Time in Rates
2:47
Changing Minutes to Seconds and Vice Versa
3:40
Changing Hours to Minutes and Vice Versa
4:41
The Big One: Seconds to Hours
5:19
Combining Multiple Rates
6:31
Which Questions to Ask
7:14
Set Up Two Equations
8:59
Solving Rates
9:32
Quick Example: Using d=rt
10:03
Solving Multiple Rates
12:29
Sequences

10m

Intro
0:00
The Basics: Sequences
0:11
When Sequences Are Just Patterns
1:14
Arithmetic Sequences
2:24
Using the Arithmetic Sequence Equation
3:11
Geometric Sequences
5:24
Using the Geometric Sequence Equation
6:08
Geometric Series that Alternate Between Negative and Positive Elements
8:02
Sets

10m 21s

Intro
0:00
The Basics: Sets
0:08
How to Represent Sets
0:25
The Union of Sets--Joining the Two Together
1:33
The Intersection of Sets--Where the Two Meet, What they Share
2:25
Sets: Intersection and Union
3:56
Venn Diagrams
6:21
Representing Two Sets
6:27
Representing the Union
7:17
Representing the Intersection
7:55
Box in Numbers Outside of the Set
8:16
Probability

8m 52s

Intro
0:00
The Basics Probability
0:10
The Scale of Probability
0:34
How to Calculate Probability
1:42
How to Solve Probability Problems
2:52
A Probability Example
4:51
Combinations and Permutations

7m 22s

Intro
0:00
The Basics: Combinations
0:11
Combination Equation
1:49
The Basics: Permutations
4:16
Permutation Equation
6:18
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