# MTH 219 Wk 5 Discussion – Functions and Variation

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**MTH 219**** Wk 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.

*Note*: All Khan Academy content is available for free at www.khanacademy.org.

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