MTH 219T Introduction to College Algebra – University of Phoenix Entire Class Solution

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MTH 219T Introduction to College Algebra

MTH 219 Week 1 Discussion – Order of Operations and Inequalities

Due Thursday

Posta response of at least 175 words to one of the discussion prompts:

Prompt 1

Watch one of the following Week 1 Videos:

• Khan Academy: “Intro to Order of Operations”
• Khan Academy: “Order of Operations Example”
• University of Phoenix: “Play of the Day”

Answer the following questions:

• How do you remember order of operations?
• If you use a calculator for computation, is order of operations still important? Why or why not?
• What are some possible outcomes when order of operations is ignored?

Prompt 2

Watch one of the following Week 1 Videos:

• Patrick Just Math Tutorials: “An Intro to Solving Linear Equations: Solving Some Basic Linear Equations”
• Patrick Just Math Tutorials: “Solving Linear Equations”

Answer the following questions:

• 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?

Due Monday

Reply to at least 2 of your classmates. Be constructive and professional in your responses.

MTH 219 Week 2 Discussion – Functions

Post a total of 3 substantive responses over 2 separate days for full participation. This includes your initial post and 2 replies to other students.

Due Thursday

Post a response of at least 175 words to one of the discussion prompts:

Prompt 1

Watch one of the following Week 2 videos:

• Khan Academy: “What is a Function”
• Patrick Just Math Tutorials: “The Vertical Line Test”
• Khan Academy: “Worked Example: Evaluating Functions from Equation”
• Khan Academy: “Worked Example: Evaluating Functions from Graph”

Answer the following questions:

• What are the various ways of representing a function?
• What methods can you use to determine whether a relation is a function? Give an example of a relation and determine if it is a function.

Prompt 2

Watch one of the following Week 2 videos:

• Khan Academy: “Intervals and Interval Notation”
• Khan Academy: “Domain and the Range from Graph”

Answer the following questions:

• Given the graph of a function, how can you determine its domain and range?
• What is an example of a real-world scenario that is a function that has a domain and range?
• What is the domain and range in your example?
• Why is it useful to determine a function’s domain and/or range for the scenario you chose?

Prompt 3

Watch one of the following Week 2 videos:

• Khan Academy: “Intro to Intercepts”
• Khan Academy: “Intro to Slope”

Answer the following question:

• In your own words, describe what the slope and y-intercept of an equation tell you about the line. Give an example in your explanation.

Due Monday

Reply to at least 2 of your classmates. Be constructive and professional in your responses.

MTH 219 Week 3 Discussion – Factoring

Post a total of 3 substantive responses over 2 separate days for full participation. This includes your initial post and 2 replies to other students.

Due Thursday

Post a response of at least 175 words to one of the discussion prompts:

Prompt 1

Watchthe following Week 3 videos:

• Patrick Just Math Tutorials: “Factoring Trinomials (a Quadratic Trinomial) by Trial and Error”
• Patrick Just Math Tutorials: “Factoring Using the Great Common Factor, GCF – Ex 1”
• Patrick Just Math Tutorials: “Factoring By Grouping – Ex 1”

Answer the following questions:

• How do you know when you’ve found the greatest common factor?
• How does the method of factoring using the greatest common factor differ from using the method of grouping?
• Which method do you prefer for factoring? Why? Include an example in your explanation.

Prompt 2

Watch one of the following Week 3 videos:

• Patrick Just Math Tutorials: “Factoring Trinomials by Trial and Error – Ex 2”
• Patrick Just Math Tutorials: “Factoring by Grouping – Ex 1”

Answer the following questions:

• 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)?
• Give two examples with your explanation. One of your examples should be for ax2 + bx + c and the other example for x2 + bx +c.

Prompt 3

Watch the following Week 3 video:

• Patrick Just Math Tutorials: “Solving Quadratic Equations by Factoring – Basic Examples”

Answer the following question:

• Is it possible to solve every quadratic equation by factoring? Why or why not?

Due Monday

Reply to at least 2 of your classmates. Be constructive and professional in your responses.

MTH 219 Week 4 Discussion – Rational Expressions

Post a total of 3 substantive responses over 2 separate days for full participation. This includes your initial post and 2 replies to other students.

Due Thursday

Post a response of at least 175 words to one of the discussion prompts:

Prompt 1

Watch the following Week 4 video:

• Khan Academy: “Proportion Word Problem: Cookies”

Answer the following questions:

• Go outside on a sunny day near a tree and measure the length of your shadow. Then measure the length of the shadow cast by the tree. Without measuring the height of the tree, how tall is the tree?
• Explain the process you used to solve this problem. (Hint: You will need to use your height to answer this question.)
• What are other applications where proportions can help you solve for unknown information that might otherwise be hard to obtain?

Prompt 2

Watch the following Week 4 video:

• Khan Academy: “Rational Equations Word Problem: Combined Rates”
• Answer the following questions:
• Think of a task that takes you a certain amount of time to complete (for example: mowing the yard, cleaning the house, etc.). Suppose your friend Sarah can complete the same task in half the time that you can. How long will it take you and Sarah to complete the task together?
• Note:You both have your own tools to complete the task.
• Explain the process you used to complete your calculations.

Prompt 3

Watch one of the following Week 4 videos:

• Khan Academy: “Intro to Rational Expression Simplification”
• Khan Academy: “Simplifying Rational Expressions: common Binomial Factors”
• Patrick Just Math Tutorials: “Rational Expressions: Writing in Lowest Terms – Ex 1”
• Khan Academy: “Adding Rational Expressions: Unlike Denominators”

Answer the following questions:

• How do you find the sum or difference of rational expressions with different denominators?
• Explain the process you use, and include an example with your explanation.

Prompt 4

Watch the following Week 4 videos:

• Khan Academy: “Multiplying Rational Expressions: Multiple Variables”
• Khan Academy: “Multiplying Rational Expressions”
• Khan Academy: “Dividing Rational Expressions”
• Patrick Just Math Tutorials: “Rational Expressions: Multiplying and Dividing. Ex 1”

Answer the following questions:

• How does multiplication and division of rational expressions compare to multiplication and division of fractions?
• How do they differ? Provide examples in your explanation.

Due Monday

Reply to at least 2 of your classmates. Be constructive and professional in your responses.

MTH 219 Week 5 Discussion – Functions and Variation

Post a total of 3 substantive responses over 2 separate days for full participation. This includes your initial post and 2 replies to other students.

Due Thursday

Post a response of at least 175 words to one of the discussion prompts:

Prompt 1

Watch one of the following Week 5 videos:

• Patrick Just Math Tutorials “Evaluating Piecewise Defined Functions”
• Patrick Just Math Tutorials: “Piecewise Functions: Find the Formula form a Graph – Ex 1”
• Patrick Just Math Tutorials: “Piecewise Functions: Find the Formula from a Graph – Ex 2”
• Patrick Just Math Tutorials: “Piecewise Defined Functions: Graphing”

Answer the following questions:

• What is an example of a real-life situation that could be represented by a piecewise function?
• Explain the various pieces of the function and how they relate to the real-life situation.

Prompt 2

Watch the following Week 5 video:

• Khan Academy: “Dividing Functions”

Answer the following questions:

• Suppose we have the quotient of functions (f/g)(x). Which values of x must be excluded from the domain of (f/g)(x)?
• Why would it be important to check for these values?
• Provide an example with your explanation.

Prompt 3

Watch one of the following Week 5 videos:

• Patrick Just Math Tutorials: “Composition of Functions”
• Khan Academy: “Evaluating Composite Functions: Using Graphs”

Answer the following questions:

• Write an equation to represent f(x) and g(x).
• Describe a method you can use to evaluate f(g(2)).
• Would the answer be the same as g(f(2))? Why or why not?

Prompt 4

Watch one of the following Week 5 videos:

• Patrick Just Math Tutorials: “Inverse Functions – The Basics!”
• Patrick Just Math Tutorials: “Finding the Inverse of a Function or Showing One Does Not Exist, Ex 2”
• Khan Academy: “Graphing the Inverse of a Linear Function”

Answer the following questions:

• How do you find the inverse of a function?
• How would you describe the method you can use to construct the inverse of a one-to-one function
• Provide an example in your explanation.

Prompt 5

Watch one of the following Week 5 videos:

• Khan Academy: “Intro to Direct and Inverse Variation”
• Khan Academy: “Direct Variation Word Problem: Filling Gas”
• Khan Academy: “Inverse Variation Word Problem: String Vibration”

Answer the following questions:

• What is a real-life example of direct variation and inverse variation?
• Explain why each example is a direct or inverse variation.

Due Monday

Reply to at least 2 of your classmates. Be constructive and professional in your responses.

MTH 219 Week 1 Math Catch Up

MTH 219 Week 2 MyMathLab® Study Plan for Week 2 Checkpoint

6.2-3 Solve application problems.

6.2-2 Factor trinomials of the form x^2+bx+c.

6.1-5 Factor by grouping.

6.1-4 Factor out the negative greatest common factor of a polynomial.

6.1-2 Find the greatest common factor.

5.2-5 Multiply monomials.

5.1-7 Solve application problems.

5.1-4 Subtract polynomials.

3.3-4 Draw lines with given slopes.

3.3-2 Compute a line’s slope.

3.2-6 Graph horizontal or vertical lines.

3.2-4 Graph a linear equation in two variables using intercepts.

3.2-3 Find the intercepts of an equation.

3.2-2 Use a graph to identify intercepts.

3.2-5 Write a linear equation using a graph.

MTH 219 Week 3 MyMathLab® Study Plan for Week 3 Checkpoint

6.3        Factoring Trinomials Whose Leading Coefficient Is Not 1

Concept and Vocabulary Check

Factor trinomials of the form ax^2+bx+c.

6.4        Factoring Special Forms

Factor the difference of two squares.

Factor perfect square trinomials.

6.6        Solve Quadratic Equations by Factoring

Solve quadratic equations by factoring.

Solve application problems.

7.1        Rational Expressions and Their Simplification

Find numbers for which a rational expression is undefined.

Simplify rational expressions.

7.2        Multiplying and Dividing Rational Expressions

Multiply rational expressions.

Divide rational expressions.

MTH 219 Week 4 MyMathLab® Week 4 Checkpoint

7.3        Adding and Subtracting Rational Expressions with the Same Denominator

Subtract rational expressions with the same denominator.

7.4        Adding and Subtracting Rational Expressions with Different Denominators

Find the least common denominator.

Add and subtract rational expressions with different denominators.

7.6        Solving Rational Equations

Solve a formula with a rational expression for a variable.

7.7        Applications Using Rational Equations and Proportions

Solve problems involving work.

7.8        Modeling Using Variation

Solve application problems.

8.1        Introduction to Functions

Evaluate a function.

8.2        Graphs of Functions

Identify the domain and range of a function from its graph.

8.3        The Algebra of Functions

Use the algebra of functions to combine functions and determine domains.

Solve application exercises.

MTH 219 Week 4 MyMathLab® Study Plan for Week 4 Checkpoint

7.3           Adding and Subtracting Rational Expressions with the Same Denominator

Subtract rational expressions with the same denominator.

7.4           Adding and Subtracting Rational Expressions with Different Denominators

Find the least common denominator.

Add and subtract rational expressions with different denominators.

7.6           Solving Rational Equations

Solve a formula with a rational expression for a variable.

7.7           Applications Using Rational Equations and Proportions

Solve problems involving work.

7.8           Modeling Using Variation

Solve application problems.

8.1           Introduction to Functions

Evaluate a function.

8.2           Graphs of Functions

Identify the domain and range of a function from its graph.

8.3           The Algebra of Functions

Use the algebra of functions to combine functions and determine domains.

Solve application exercises.

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MTH 219 Week 5 Final Exam in MyMathLab®

8.4           Composite and Inverse Functions

Find the inverse of a function.

Solve application problems.

9.2           Compound Inequalities

Solve compound inequalities involving and.

10.1        Radical Expressions and Functions

Evaluate cube roots and cube root functions.

10.2        Rational Exponents

Use the definition of a^(m/n).

Simplify radical expressions using rational exponents.

10.3        Multiplying and Simplifying Radical Expressions

Use factoring and the product rule to simplify radicals.

Multiply radicals and then simplify.

10.4        Adding, Subtracting, and Dividing Radical Expressions

Simplify radical expressions before adding or subtracting.

10.5        Multiplying with More than One Term and Rationalizing Denominators

Use polynomial special products to multiply radicals.

10.6        Radical Equations

Solve radical equations.