Unit+2+Virtual+Homework

For the following three functions, complete a table of values for x values from -5 to 5 in your classroom binder and use your table of values to graph each function. You will find the three function in the document below. After evaluating for x values of -5 to 5 and graphing, answer the following questions in your virtual notebook.
 * __ Unit 2 Lesson 1 __**
 * What type of function is f(x)? g(x)? and h(x)? Explain.
 * What observations did you make about the table of values and graph of f(x)? Explain how this relates to the function and why you think this happened.
 * What observations did you make about the table of values and graph of g(x)? Explain how this relates to the function and why you think this happened.
 * What observations did you make about the table of values and graph of h(x)? Explain how this relates to the function and why you think this happened.
 * Look up the mathematical definition for domain and write what domain means in your own words. How do your observations made about each function and table of values relate to this definition? Explain.
 * What do your think would be an appropriate domain for a function representing the population of deer from the years 1975-2005? Explain.

__** Unit 2 Lesson 2 **__ Read pages 91-96 in your text book. Take notes on the following terms in your classroom binder. You will need these notes to complete tomorrow's activity. **Local maximum:** **Local minimum:** **Increasing:** **Decreasing:** **Constant:** **Continuity:** **Removable Discontinuity:** **Jump Discontinuity:** **Infinite Discontinuity:** In your virtual notebook, answer the following questions about the graph provided. You should refer to the defnitions of the terms above to help you answer the questions.




 * Find f(-3), f(1), when f(x) = 2, and f(x) = -2
 * Where is this function increasing?
 * Where is the function decreasing?
 * Where is the function constant?
 * How can you tell on a graph where a function is increasing, decreasing or constant?
 * Is the function continuous? Explain.
 * Find all local extrema of the function. What does it mean to ba a local maximum? What does it mean to be a local minimum? Can a function have more then one local maximum or minimum? Explain.

The following graphs represent even and odd functions. I sorted the functions for you according to whether the function is an even function or an odd function. __**Even Functions**__
 * __ Unit 2 Lesson 3 __**
 * __Odd Functions__**

In your virtual notebook answer the following questions:
 * Based on the classifications, when given a graphical representation what do you observe about all of the even functions?
 * Based on the classifications, when given a graphical representation what do you observe about all of the odd functions?
 * Do you think a function always has to be odd or even? Explain. Support your answer with an example if necessary.
 * How can you tell if a function is even or odd looking at a table of values? Explain.
 * How can you prove a function is even or odd algebraically? What steps should you take to prove whether a function is even of odd algebraically using the definition? Explain.


 * __ Unit 2 Lesson 10 __**
 * 1. In your own words, write the steps of performing a graphical transformation. Include any key reminders you think a students will forget in your description. **


 * 2. The graph of a function f(x) is illustrated. Use the graph of f(x) to perform the following graphical transformations. You do not need to show the shifted graph, you just need to list the 6 corresponding points. Answer each part seperately. **

(a) H(x) = f(x + 1) -2 (left 1 and down 2 units) (b) Q(x) = 2f(x) (stretched by 2) (c) P(x) = -f(x) (reflection over x-axis)


 * 3. Suppose that the //x//-intercepts of the graph of f(x) are -5 and 3. Explain your thinking process or what helped you arrive at your answers. **

(a) What are //x//-intercepts if y = f(x+2)? (shifted to the left two units)

(b) What are //x//-intercepts if y = f(x-2)? (shifted to the right two units)

(c) What are //x//-intercepts if y = 4f(x)? (stretched vertically by 4)

(d) What are //x//-intercepts if y = f(-x)? (reflected over the y-axis)


 * 4. Suppose that the function f(x) is increasing on the interval (-1, 5). Explain your thinking process or what helped you arrive at your answers. **

(a) Over which interval is the graph of y = f(x+2) increasing? (left 2 units)

(b) Over which interval is the graph of y = f(x-5) increasing? (right 5 units)

(c) Over which interval is the graph of y = f(x)-1 increasing? (down 1 unit)

(d) Over which interval is the graph of y = -f(x) increasing? (reflected over x-axis)

(e) Over which interval is the graph of y = f(-x) increasing? (reflected over y-axis)