Unit+2+Virtual+Notebook

__**Unit 2 Lesson 1**__ >> g(x) is a square root function, starts off near the x axis and rises with one curve >> h(x) is an odd function, one half is reflected over the x axis
 * What type of function is f(x)? g(x)? and h(x)? Explain.
 * f(x) is a parabola, it has an even exponent on the leading coefficient
 * 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.
 * The values of the negative and positive x's have basically the same f(x) y but its negative or positive.This relates to the function because its a parabola and parabolas have the same symmetry and distance between.
 * 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.
 * The values of the negative g(x) come up as "error" on the calculator because it is impossible to have a negative number inside a square root sign. The positive numbers from 0-5 are decimals because each number is squared rooted and none of them are perfect squares. This relates to the function because it starts from -1 and looks similar to a linear line but it's increasing by the decimal.
 * 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.
 * The values of basically all numbers are in decimal form but -3 comes up as "error". This relates to the function because it's similar to a piecewise. The two lines on the graph are not connected because one goes the other way and vise versa.
 * 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.
 * A set of all possible input x values that are bounded. My observations of each function and table of values relate to this definition because the numbers that have a f(x), g(x) or h(x) are all possible but the ones with "error" are not possible or considered in the "domain"
 * What do your think would be an appropriate domain for a function representing the population of deer from the years 1975-2005? Explain.
 * I think the appropriate domain function representing the population of deer from the years 1975-2005 would be an equation f(x) that relates to the inequality 1975> X = 5 X = -1 >> y-value decreasing; x-value is increasing. >> y-value stays the same; x-value is increasing. >> Local min - negative infinity; Graph reached negative infinity.
 * Find f(-3), f(1), when f(x) = 2, and f(x) = -2
 * F(-3) = 4F(1) = -2
 * Where is this function increasing?
 * (3, -2) to (5, 2)
 * Where is the function decreasing?
 * (-infinity, -1) to (-1, -2) and (5, 2) to (5, infinity)
 * Where is the function constant?
 * (-1, -2) to (3, -2)
 * How can you tell on a graph where a function is increasing, decreasing or constant?
 * y-value increasing; x-value is increasing.
 * Is the function continuous? Explain.
 * Yes, because there is no maximum or minimum.
 * 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.
 * Local max - infinity; Graph reached infinity.

**__Unit 2 Lesson 3__** 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**__
 * __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?
 * It is always symmetrical over the y-axis
 * Based on the classifications, when given a graphical representation what do you observe about all of the odd functions?
 * It is symmetrical over the y or x axis, depending on the graph.
 * Do you think a function always has to be odd or even? Explain. Support your answer with an example if necessary.
 * I don' think a function always has to be odd or even because they both have the same characteristics that they are both symmetrical over the y or x axis.
 * How can you tell if a function is even or odd looking at a table of values? Explain.
 * Odd - Same positive/negative values but has different signs frequently
 * Even - Same positive/negative values -5 - 0 and 0- 5
 * 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.
 * The original would just be f(x) but you would have to plug in the equation in both -f(x) and f(-x). If the results of both are the same then it is odd but if the results of both are different then it is even.

**__Unit 2 Lesson 10__** 1) Find the value of h, shift x values 2) Reflect over the y-axis or x-axis. 3) Stretch - |//x|// > 1. Shrink - //|x|// < 1. 4) Find the value of k, shift y values
 * 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. **

(a) H(x) = f(x + 1) -2 (b) Q(x) = 2f(x) (c) P(x) = -f(x)

x H(x) -3 0 -2 .8  -1 -2  0 -1.5  1 -1  2 -5

x Q(x) -2 4 -1 3.6  0 0  1 1  2 2  3 3

x P(x) -2 -2 -1 -1.8  0 0  1 -.5  2 -1  3 -1.5


 * 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)? x intercept = -2 and 5

(b) What are //x//-intercepts if y = f(x-2)? x intercept = - 7 and 1

(c) What are //x//-intercepts if y = 4f(x)? x intercept = -5 and 3

(d) What are //x//-intercepts if y = f(-x)? x intercept = 5 and -3


 * 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? Increasing (1, 7)

(b) Over which interval is the graph of y = f(x-5) increasing? Increasing (-6,0)

(c) Over which interval is the graph of y = f(x)-1 increasing? Increasing (-1,5)

(d) Over which interval is the graph of y =- f(x) increasing? Increasing (-1,5)

(e) Over which interval is the graph of y = f(-x) increasing? Increasing (1,5) <span style="font-family: 'Times New Roman',Times,serif;">