# MAT 219 All Participations

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MAT 219

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MAT 219 Week 1 participation Order of Operations
What is the order of operations? How does it affect the value of an expression, and why is that important? Include a professional or everyday-life example in your answer.

MAT 219 Week 1 participation Integers, rational, real and irrational numbers
Explain the main differences between integers, rational numbers, real numbers, and irrational numbers. How are these used in everyday life? How would you explain the use of each to someone who did not know about the differences?

MAT 219 Week 1 participation Expression vs. Equation
Explain the differences among an English sentence, an algebraic expression, and an algebraic equation. How can you convert from one of these forms to another?

MAT 219 Week 1 participation Chapter 1
What area in chapter one was easiest to understand and why ?

MAT 219 Week 2 participation Cartesian Coordinate System
Explain how the Cartesian coordinate system unites algebra and geometry.

MAT 219 Week 2 participation Coordinates equal to zero
For any linear equation, why is it true that for the x-intercept, the y-coordinate is zero and for the y-intercept, the x-coordinate is zero?

MAT 219 Week 2 participation Linear Equations
What are some of the similarities and differences between linear equations with one variable and linear equations with two variables?

MAT 219 Week 2 participation Solving Linear Equations
When solving linear equations, why do we need to perform the same operation to both sides of the equation? What would happen if we only performed operations to one side of the equation?

MAT 219 Week 2 participation Solving Linear Inequalities
What are the steps in solving linear inequalities?

MAT 219 Week 2 participation Graphed Data
Explain the relationship between graphed data and linear equations.  Use a specific example to demonstrate how this relationship helps to model data.

MAT 219 Week 2 participation Slope
Define slope.  Use a specific example to explain how slope allows you to calculate the rate of change in various situations.

MAT 219 Week 2 participation Linear Inequality
How is the approach to solving a linear inequality similar to solving a linear equation? When is the approach different? What process do you use when determining which side of an inequality to shade?

MAT 219 Week 3 participation Comparing methods
Compare the substitution, addition and elimination methods for solving linear equations.  Under what circumstances would a certain method be recommended?

MAT 219 Week 3 participation Patterns of Our World
Explain how systems of linear equations in two variables reveal hidden patterns of our world.

MAT 219 Week 3 participation Ordered Pairs
How can you determine whether an ordered pair is a solution of a linear system?

MAT 219 Week 3 participation Substitution
Explain the application of the substitution method to supply and demand economics.

MAT 219 Week 3 participation Graphs of Linear Equations
What is the minimum information needed to be able to graph a linear equation? What process do you go through to graph a linear equation? Give an example, starting with a linear equation, and explain the steps you would use to graph it.

MAT 219 Week 3 participation Using slope to determine solution
Without graphing, can you use the slope to determine whether there is a solution for a system of two linear equations in two unknowns? How?

MAT 219 Week 3 participation Example using Graphs
Give an example of a problem that can be solved using graphs of linear systems. ( 50 word minimum)

MAT 219 Week 3 participation x- or y-intercept
If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x- or y-intercept. Will that always be true for that situation?

MAT 219 Week 4 participation Numeracy
What is numeracy?  Explain the advantages and disadvantages of numeracy for a democratic society.  Do you feel our educational system does a sufficient job of promoting social numeracy?  Why or why not?

MAT 219 Week 4 participation Product and Power Rules
Explain the product rule, power rule, and products to powers rule.  Why are these rules important when multiplying polynomials?

MAT 219 Week 4 participation Polynomial Vocabulary
Explain the vocabulary used to describe polynomials.  Why is knowledge of vocabulary important in the study of mathematics and other disciplines?

MAT 219 Week 4 participation Greatest Common Factor
What is the greatest common factor? How do you know when you have found the greatest one? How does the method of factoring using the greatest common factor differ from using the method of grouping?

MAT 219 Week 4 participation FOIL Method
What is the FOIL method for multiplying polynomials?  Under what circumstances should this method be followed?

MAT 219 Week 4 participation Distinguish between terms and factors
Why is it important to distinguish between terms and factors?

MAT 219 Week 4 participation Synthetic division
How would you explain the performance of synthetic division to someone else? Use the problem (2x3 - 3x2 - 11x + 7)/(x + 3) to support your explanation.

MAT 219 Week 4 participation Message expanded.Message readPolynominals: Adding, Subtracting, Multiplying & Simplifying
You might have heard you can only combine like terms. Why is this?

What if a classmate didn't believe you?  For example what conclusions would you be able to draw if 2x + 1 = 3x for all x?

MAT 219 Week 5 participation Trinomials
Choose three integers a, b, and c--feel free to choose negative numbers. Use a, b, and c to create a trinomialax2 + bx + c. Can you factor this trinomial?  How would you create a trinomial that will factor?

MAT 219 Week 5 participation Factoring
What is factoring?  How does it relate to the reversal of multiplying polynomials?  Support your answer with specific examples.

MAT 219 Week 5 participation Combinations of Factors
Explain a way to eliminate some of the combinations of factors for x2 + bx + c when c is positive?  Provide an example in your explanation.

MAT 219 Week 5 participation Quadratic Equations
Why is it a good idea to factor a quadratic equation before you solve?

MAT 219 Week 5 participation Factoring Trinomials
Explain the differences between the techniques used to factor trinomials whose leading factor is 1 and the techniques used to factor trinomials whose leading factor is not 1.

MAT 219 Week 5 participation Checking the answer
How can you check the answer to a factoring problem such as 10x2 - 13x - 3 = (2x - 3)(5x + 1)?

MAT 219 Week 5 participation Factoring Polynomials
What process do you use to factor polynomials when the leading coefficient is not 1 (example: ax2 + bx + c)? How does this differ from factoring polynomials when the leading coefficient is 1 (example: x2 + bx + c)? Is it possible to solve every quadratic equation by factoring? Why?

MAT 219 Week 6 participation Simplifying an Expression
When you simplify a rational expression, why are the numerator and the denominator factored? Why do you need a least common denominator when adding and subtracting rational expressions?

MAT 219 Week 6 participation Types of Variation between x and y
What is an example from professional or everyday life that describes the types of variation between two variables x and y?

MAT 219 Week 6 participation Cost Benefit Examples
Explain some applications of fractional expressions to economic cost benefit analyses.

MAT 219 Week 6 participation Using Rational Equations
Explain some of the applications for using rational equations and proportions for solving problems involving motion, work, proportions, or similar triangles.

MAT 219 Week 6 participation Simplifying rational expressions
What process do you use to simplify rational expressions?

MAT 219 Week 6 participation Rational Expressions
What is a rational expression? How would you explain this concept to someone unfamiliar with it?

MAT 219 Week 6 participation Comparing Multiplication and Division of Rational Expressions
How does multiplication and division of rational expressions compare to multiplication and division of fractions? How do they differ?

MAT 219 Week 7 participation Composite Functions
Suppose you have two functions f and g and you use them to form a composite function. Under what conditions will they be the same? Include a numerical example in your answer.

MAT 219 Week 7 participation Graphing a Function vs. Graph of a Function
How would you explain the difference between the method used for graphing a function from how to determine the domain and range from the graph of a function?

MAT 219 Week 7 participation Domain and Range
Using a specific example, explain the differences between the domain and range with respect to a relation.  How can we determine if a relation is also a function?

MAT 219 Week 7 participation Inverses
Explain how to determine if two functions are inverses of each other.

MAT 219 Week 7 participation Information from graphs of a function
Explain the types of information about a function that can be obtained from a graph of the function.

MAT 219 Week 7 participation Square Roots
Does every positive real number have two square roots? Why or why not?

MAT 219 Week 7 participation Vertical Line Test
What is the Vertical Line Test?

MAT 219 Week 7 participation Performing Operations on Functions

What is the most difficult aspect of performing operations on functions? How can you overcome?

MAT 219 Week 8 participation Inverse of One-to-One Function
Describe the method you can use to construct the inverse of a one-to-one function.

MAT 219 Week 8 participation What is a piecewise function?
What is a piecewise function? Create a numerical example and explain how your example could represent a realistic situation.

MAT 219 Week 8 participation Examples of Inverse Functions
What are realistic examples of inverse functions?

MAT 219 Week 8 participation Inverse of a Function
How do you find the inverse of a function?

MAT 219 Week 8 participation Radicals
Explain why    is negative when n is odd and a is negative. What happens if n is even and a is negative? Why?

MAT 219 Week 8 participation Product Rule for Radicals
Explain the Product Rule for Radicals.  Can you use the product rule to simplify radicals with different indices, such as

MAT 219 Week 8 participation Simplified Radical Expressions
Explain why    is not simplified. What do we mean when we say a radical expression is simplified?

MAT 219 Week 9 participation Explaining Even and Odd Root Radical Functions
How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function? How would you change your explanation for someone who had taken high school algebra?

MAT 219 Week 9 participation Laws of Radicals
What law of radicals allows you to treat radical expressions as exponential expressions? How would you explain this to someone else and how would you explain adding like radicals? Include an example with your explanation. Use the following notation for square root: sqrt(3).

MAT 219 Week 9 participation Rationalized Denominator
When a radical expression has its denominator rationalized, we change the denominator so that it no longer contains any radicals. Doesn't this change the value of the radical expression? Explain.

MAT 219 Week 9 participation Isolating the Radical Term
In solving   , why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

MAT 219 Week 9 participation Extraneous Solution to Radical Equation
What is an extraneous solution to a radical equation?

MAT 219 Week 9 participation Rationalizing th Denominator
What is the role of the quotient rule of radicals when rationalizing the denominator?