Basic Algebra

Auston B Cron

This collection is for applets which are for simple algebra lessons.

Table of Contents

  1. Basics of Graphing
    1. Basic Trig -360 x 360
    2. Blank Inverse Propery Study
    3. Domain and Range of any Function
    4. EXERCISE: Reading the coordinates
    5. Expressing Function Values as Lengths of Line Segments
    6. Graphing {Completing the Square}
    7. Pythagorean Triple Generator
    8. Writing coordinates
    9. Read and Submit Coordinates Quadrant I
    10. Quadratic Lesson Creator Part 2
    11. General Linear Equation
    12. General Quadratic Equation
  2. Domain and Range
    1. Domain and Range Using Beads
    2. Domain and Range: Properties of the function
    3. Domain and Range of any Function
    4. Domain and Range of a Relation
  3. Function Arithmetic
    1. Adding Functions
    2. Subtracting Functions
    3. Multiplying Functions
    4. Dividing Functions
    5. Composition of Functions
    6. Function Composition (Impoved)
    7. Quadratic Lesson Creator Part 1
    8. Quadratic Lesson Creator Part 3
    9. Venn Diagram Real Numbers
  4. Basic Square Cubes & their Inverses
    1. Squares and Cubes: Favorites of Mathematics
    2. Square and Cube Roots: Favorites of Mathematicians
  5. Systems of Equations
    1. Simple Linear System of Equations
    2. Gauss-Jordan 2x2 Elimination
    3. Gauss-Jordan Elimination
    4. System of Equation (2x3): Elimination
    5. System of Equation (2x4): Elimination
  6. Exponential and Logorithmic Functions
    1. EXERCISE: Determine Equation of Exponentatial Functions (2)
    2. EXERCISE: Determine Equation of Logarithmic Functions
    3. Exponential and Logarithmic Function Graphs (base > 1)
    4. Exponents and Logarithms a Study of Inverses
  7. Function Properties
    1. Family of Functions
    2. Graphing and Transforming Trigonometry Functions
    3. Greatest Integer Function
    4. Inverse Function Basics
    5. Quadratic: Compare Standard to Vertex Forms
    6. Quadratic: Compare Vertex to Standard Forms
    7. Rational Functions and their Asymptotes
    8. Standard Form of Parabolas
    9. Vertex Form of Parabolas
    10. Standard Form of Cubic
    11. Vertex Form of Cubic
    12. Transformations: Basic Family of Functions
    13. Integer Base/Exponents
  8. Piecewise Functions
    1. 3 Part Piecewise Function
    2. 1, 2, or 3 Part Piecewise Function
    3. 1,2,3,4,5 Part Piecewise Function
    4. Function Properties: Random Piecewise Function
    5. 3 Piecewise Functions: Sliders
    6. Solving Absolute Value Inequalities Visually, Greater Than
    7. Solving Absolute Value Inequalities Visually, Less Than

1.

Basics of Graphing

  • 1. Basic Trig -360 x 360
  • 2. Blank Inverse Propery Study
  • 3. Domain and Range of any Function
  • 4. EXERCISE: Reading the coordinates
  • 5. Expressing Function Values as Lengths of Line Segments
  • 6. Graphing {Completing the Square}
  • 7. Pythagorean Triple Generator
  • 8. Writing coordinates
  • 9. Read and Submit Coordinates Quadrant I
  • 10. Quadratic Lesson Creator Part 2
  • 11. General Linear Equation
  • 12. General Quadratic Equation

1.1.

Basic Trig -360 x 360

This is a blank page set for students to graph trig functions easily by plotting the points by using the point tool. When finished plotting the student should try to write the function graphed.
The degree symbol is require for graphing: sin(x°), cos(x°), tan(x°) {PC can use <alt><o> or symbol menu α }[br][br]Available for all who desire to use...
– Auston B Cron

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

2.

Domain and Range

  • 1. Domain and Range Using Beads
  • 2. Domain and Range: Properties of the function
  • 3. Domain and Range of any Function
  • 4. Domain and Range of a Relation

2.1.

Domain and Range Using Beads

Using beads to teach domain and range is demonstrated by the LTF in some of their lessons. This demonstration is a sample of using GeoGebra to advance the lesson to multiple functions.
Domain and Range Using Beads
– Auston B Cron

2.2.

–

2.3.

–

2.4.

–

3.

Function Arithmetic

  • 1. Adding Functions
  • 2. Subtracting Functions
  • 3. Multiplying Functions
  • 4. Dividing Functions
  • 5. Composition of Functions
  • 6. Function Composition (Impoved)
  • 7. Quadratic Lesson Creator Part 1
  • 8. Quadratic Lesson Creator Part 3
  • 9. Venn Diagram Real Numbers

3.1.

Adding Functions

This applet will illustrate the addition of two functions, f(X) anf g(x). [br][br]You can display two functions by using the show check box for each equation. The default equations are f(x) = x2 and g(x) = -2x, you can enter equations of your choice by entering the function of x of your choice. [br][br]f(x) will graph in red, and g(x) will graph in green. The addition will displayed as h(x) and will display in blue. By clicking on the appropriate check box, you will be able to display each graph separately or together.[br][br]Prior to displaying the solution function h(x), use the point tool to locate points on the grid for h(x), i.e., read the y-values of f(x) and g(x), perform the arithmetic operation chosen, and plot the y-value of h(x). Select at least 5 points to illustrate the trace of h(x). If using SMART or Promethian board have students find and plot the points. Hide f(x) and g(x) to allow users to determine a pattern before displaying f(x).
Adding Functions
– Auston B Cron

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

4.

Basic Square Cubes & their Inverses

  • 1. Squares and Cubes: Favorites of Mathematics
  • 2. Square and Cube Roots: Favorites of Mathematicians

4.1.

Squares and Cubes: Favorites of Mathematics

Mathematics teachers and textbook authors utilize the perfect squares and cubes of numbers in creating their problems for students to use on a test or from a set of problems in a textbook.[br][br]Here we can explore the set of perfect squares and cubes by moving the n-slider. Each square of n thru 25 and cube of n through 10 are favorites of creators of problems for students. [br][br]Use this site to help you learn these values.
Squares and Cubes: Favorites of Mathematics
– Auston B Cron

4.2.

–

5.

Systems of Equations

  • 1. Simple Linear System of Equations
  • 2. Gauss-Jordan 2x2 Elimination
  • 3. Gauss-Jordan Elimination
  • 4. System of Equation (2x3): Elimination
  • 5. System of Equation (2x4): Elimination

5.1.

Simple Linear System of Equations

This lesson will assist student in learning to solve simple linear systems of equations in two variables by elimination. The graphical solution is demonstrated as well.[br]The process is completed by manipulating the sliders to multiply or divide the coefficient to get either the x or y values to be the same (opposite).[br][br]n and m are values from 1-10, r and s multiply the line by -1, and i and j turn the n and m values into divisors.[br][br]Your assignment is to copy 10 original equation sets, eliminate the x-values and solve for y (copy the eliminated system), reset sliders to eliminate y-values and solve for x (copy the eliminated system). After writing the solution, check you solution by clicking on Show Intersection to verify you are correct. Also, you may check you solution by the graphical solution.
Simple Linear System of Equations
– Auston B Cron

5.2.

–

5.3.

–

5.4.

–

5.5.

–

6.

Exponential and Logorithmic Functions

  • 1. EXERCISE: Determine Equation of Exponentatial Functions (2)
  • 2. EXERCISE: Determine Equation of Logarithmic Functions
  • 3. Exponential and Logarithmic Function Graphs (base > 1)
  • 4. Exponents and Logarithms a Study of Inverses

6.1.

EXERCISE: Determine Equation of Exponentatial Functions (2)

TASK: Find the equation for the given exponential function of the type f (x) = a â‹… bx.[br][br]If you can not read the equation, let you display help and try your hand the equation of the blue graph to approximate. If you have found the correct parameters, you receive a message.
EXERCISE: Determine Equation of Exponentatial Functions (2)
– Auston B Cron

6.2.

–

6.3.

–

6.4.

–

7.

Function Properties

  • 1. Family of Functions
  • 2. Graphing and Transforming Trigonometry Functions
  • 3. Greatest Integer Function
  • 4. Inverse Function Basics
  • 5. Quadratic: Compare Standard to Vertex Forms
  • 6. Quadratic: Compare Vertex to Standard Forms
  • 7. Rational Functions and their Asymptotes
  • 8. Standard Form of Parabolas
  • 9. Vertex Form of Parabolas
  • 10. Standard Form of Cubic
  • 11. Vertex Form of Cubic
  • 12. Transformations: Basic Family of Functions
  • 13. Integer Base/Exponents

7.1.

Family of Functions

In this activity you will use sliders to investigate the effects of the parameters of a, h, and k on parent functions. You will initially see the basic (parent) function. [br]You will change the function study by selecting NEXT or PREV.[br][br]Function in this study are Quadratic, Absolute Value, Square Root, Exponential, Logarithm, Cubic, and Sine.
TI-Nspire Activity Family of Functions http://www.timath.com/algebra2/998[br][br][PDF] Student Activity Sheet modified for GeoGebra. [br]http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Families_of_Functions_Student_GG.pdf[br][br]This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.
– Auston B Cron

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

7.9.

–

7.10.

–

7.11.

–

7.12.

–

7.13.

–

8.

Piecewise Functions

  • 1. 3 Part Piecewise Function
  • 2. 1, 2, or 3 Part Piecewise Function
  • 3. 1,2,3,4,5 Part Piecewise Function
  • 4. Function Properties: Random Piecewise Function
  • 5. 3 Piecewise Functions: Sliders
  • 6. Solving Absolute Value Inequalities Visually, Greater Than
  • 7. Solving Absolute Value Inequalities Visually, Less Than

8.1.

3 Part Piecewise Function

Piecewise functions have two or more function parts making them up. This is a demo of a 3 part function.[br][br]You can enter any function into f1(x), f2(x), and f3(x) along with its matching domain.[br][br]You may need to place your mouse on the origin, press <shift> and scroll in/out to ZOOM the graph.[br][br]Also, holding <shift> while dragging the mouse will move the entire graph.
3 Part Piecewise Function
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.[br][br]Shows various shading options.
– Auston B Cron

8.2.

–

8.3.

–

8.4.

–

8.5.

–

8.6.

–

8.7.

–

Information