Determine Domain and Range Essay Example for Free

Determine Domain and Range Essay the graph by going to the graph window, clicking on File, scrolling down to copy to clipboard and clicking on copy to clipboard. In your opened Word document click on Edit/Paste. Below the pasted graph, answer the following questions. Express your answer using inequalities or interval notation. (1) What is the domain of ? The domain of is the set of all real numbers. (-? , +? ) (2) What is the range of ? The range of is the set of all real numbers greater or equal to zero ( ). [0, +? ) B. On the same graph in Winplot, repeat the procedure above for a new function and add the graph to the previous graph. Copy and paste the new graph into the Word document. Below the new graph, answer the questions below. Express your answer using inequalities or interval notation. (1) What is the domain of ? The domain of is the set of all real numbers. (-? , +? ) (2) What is the range of ? The range of is the set of all real numbers greater or equal to two ( ). [2, +? ) C. Again, on the same graph in Winplot that contains the other two functions, graph a third function . Copy and paste the graph into the Word document. Below the graph answer the questions below. Express your answer using inequalities or interval notation. (1) What is the domain of ? The domain of is the set of all real numbers. (-? , +? ) (2) What is the range of ? The range of is the set of all real numbers greater or equal to minus three ( ). [-3, +? ) D. By observing the answers you have submitted for parts A, B, and C, make a general statement about the domain and range for a function of the type: , for a 0 and also for a 0. The domain of is the set of all real numbers. (-? , +? ) The range of is the set of all real numbers greater or equal to a ( ). [a, +? ) 2. Graphing a Linear Function A. Use Winplot to graph the following linear functions on the same graph. See problem one for how to graph in Winplot and paste the graphs into Word. Copy and paste the graph into the Word document. Below the graph answer the questions shown below. (1) Of the three equations, which has the steeper graph? What is its slope? Of the three equations, has the steeper graph. The slope of is 7/4. (2) What point do all three lines have in common? (Express as an ordered pair. ) All three lines have point (0, 0) in common. B. Use Winplot to graph the following three linear functions on the same graph. Copy and paste the graph into the Word document. Below the graph answer the questions shown below. (1) Compare the graph of the first equation to those of the other two equations. What effect does adding the +1 (second equation) and then the -2 (third equation) have on their graphs as compared to the original graph (first equation )? The graph of equation is parallel to graph of equations and . Adding the +1 to the original graph of , moves graph up by 1 unit. Adding the -1 to the original graph of , moves graph down by 2 unit. (2) Complete the following sentence: The word which best describes the three lines in the graph is _Parallel__. (choose one: perpendicular, intersecting, or parallel. ) (3) What is the slope of each of the three lines? The slope of each of the three lines is ?. (4) What is the y-intercept for each line, respectively? Give the ordered pair for each. The y-intercept for lines , , and are (0,0), (0,1), and (0, -2), respectively. C. Using Winplot, graph the functions y = 3 and y = | x | on the same graph. Copy and paste the graph into the Word document. Below the graph answer the questions shown below. (Enter y = abs(x) into Winplot to graph the second equation). (1) Describe the shape of the graph y = | x |. The shape of the graph is similar to ‘V’. Since y = |x|, therefore the value of y will be always positive and the graph will be represented by equations of two line that forms ‘V’ shape at (0,0). (2) What orientation (horizontal or vertical) does the line y = 3 have? The line y = 3 have horizontal orientation. (3) List the ordered pairs of the 3 points which form a triangle in the picture, (-3, 3), (0,0), and (3,3) (4) Using the formula A = ? bh, what is the area of the triangle pictured? A = (1/2)bh = (1/2)*6*3 = 9 square units. 3. Match the Graph of a Function with its Equation A. Copy and paste all six graphs shown below into your Word document. Label each graph with the appropriate equation from the following list. Use Winplot to help determine the correct match of equation to the given graph.