Unit+II+Virtual+Notebook+Responses

=Unit Two =

Lesson 1:
-They are all fuction notations, the y-value. -The values of the f(x) function went down when the negative values were closer to zero; as the values went into positive numbers the valuess increased at the same values that they decreased. This relates to the function because when squaring a negative number, it has the same value as squaring a positive number. -The input value did not work in the function for those values that resulted in an output value inside the radical which was negative. This is because if you multiply a number by itself, it will never be a negative number. -I observed that there were two seperate graphs for one function due to the function only having one value that cannot be used as in input value, 3, because of a denominator never being able to eqaul zero in a fraction. -An appropriate domain for a function representating the population of deer from the years of 1975-2005 would be 0 to 30 due to it being thirty years in total. Therefore zero would equal 1975 while 30 would equal 2005.
 * 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.**
 * -**Domain: set of all of possible input values of x, with every input, there is an output. However, the domain may be limited.
 * What do your think would be an appropriate domain for a function representing the population of deer from the years 1975-2005? Explain.**

Lesson 2:
-f(-3) = 5 -f(x) = 2 when x = 5 -f(x) = -2 when x = -1 (3,5) (-infinity, -1) U (5, infinity) (-1,3) A graph is increasing if the line is going up, a graph is decreasing if the graph is facing downwards, and the graph is constant when there is a straight line in the graph. The function is continuous because there are no breaks in the graph. Local Max: Highest point of the graph - (5,2) Local Min: Lowest point of the graph - None You can have more than one max or min because there can be more than one point on the graph.
 * 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.**

Lesson 3:
__ **Even Functions** __
 * __Odd Functions__ **

In your virtual notebook answer the following questions: -The axis of symmetry is along the y-axis. -The axis of symmetry is the origin - (0,0) -A function does not always have to be odd or even because a graph of a function does not have line of symmetry anywhere, it could be neither. You can tell if a function is even or odd on a table of values by if the x values are negative when the y values are negative and the x values are positive when the y values are positive, it is __odd.__ And if the positive and negative x-values have the same y-values the graph is __even.__ A function can proven if it is even or odd algebraically if you use this equation: __To prove if equation is odd:__ f(-x) = -f(x) - plug in the negatives in the right places! __To prove if equation is even:__ f(-x) = f(x)
 * 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.**


 