FOR GENIUS 2006

Here are two Math problems for this Assignment. 
Problem 1:
Graph each relation, and state the domain and range.
a) x = y2
b) x = | y ? 3 |
Solution
a) Because the equation x = y2 expresses x in terms of y, it is easier to choose the y-coordinate first and then find the x-coordinate:
Figure 11.16 shows the graph. The domain is [0, ?) and the range is (??, ?).
Figure 11.16
b) Again we select values for y first and find the corresponding x-coordinates:
Plot these points as shown in Fig. 11.17. The domain is [0, ?) and the range is (??, ?).
Figure 11.17
Now do Exercises 45–56
Note that y = x2 is a function and x = y2 is not a function because we have agreed that x is always the independent variable and y the dependent variable. You can determine the y-coordinate from x in y = x2, but y can’t be determined from x in x = y2.If we use variables other than x and y, then we must know which is the independent variable to decide if the equation is a function. For example, if W = a2 and a is the independent variable, then W is a function of a.

Problem 2:
Graph the function, and state the domain and rangey 
y = 2 | x |

There are many ways to go about solving math problems. For this assignment you will be required to do some work that will not be included in the discussion. First, you need to graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
• Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)
• Discuss the general shape and location of each of your graphs.
• State the domain and range for each of your equations. Write them in interval notation.
• State whether each of the equations is a function or not giving your reasons for the answer.
• Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
• Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.): 
o Function 
o Relation 
o Domain 
o Range 
o Transformation 

Read the following instructions in order to complete this assignment:

1. We define the following functions:

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f(x)=2x+5 g(x)=x^2-3 h(x)=7-x/3

· Compute (f – h)(4).

· Evaluate the following two compositions: (fog)(x) and (hog)(x).

· Transform the g(x) function so that the graph is moved 6 units to the right and 7 units down.

· Find the inverse functions f^-1(x) and h^-1(x).

· Your solutions to the above problems, making sure to include all mathematical work for both problems, as well as explaining each step.

· A discussion of the applicability of functions to the real world, based upon your reading of Chapter 11 of Elementary and Intermediate Algebra. Be sure to use specific examples, a brief discussion of why your examples are important, and to cite your sources.