Click on , choose Y =F(X), and specify 1 function and hit enter. Type the function as follows: x^(1/3) and hit enter. Use this window: Min X: –4, Max X: 4, Min Y: –4, Max Y: 4.Write the equation of each vertical asymptote.Trigonometric Functions and Transformations: Graph the function from Example 4, page 51.Rules of exponentsClick on , choose Y =F(X), and specify 1 function and hit enter. Type 2x/(x–3) and hit enter. Use this window: Min X: –8, Max X: 8, Min Y: –8, Max Y: 8 and hit enter.SECTION 2.1: the Tangent and Velocity Problems1.1 GROUP EXERCISES SECTION 1.1: FOUR WAYS TO REPRESENT A FUNCTIONA function f is a rule that assigns to each element x in a set A exactly one element, called( )f x, in a set B.1.1 GROUP EXERCISES1. The graphs of fand gare given.a. State the values of (3)fand ( 1)g .b. For what values of x is ( ) ( )f x g x?c. Estimate the solution of the equation ( ) 1f x .d. State the approximate domain and range of g.e. On what interval(s) is f decreasing?f. On what interval(s) is f concave up?2. Sketch the graph of a function defined for 0x  with all of the following properties:a. ( )f x is decreasing on the interval ( )0,3.b. ( )f x is increasing on ( )3,�.c. ( )f x is concave up on ( )0,5.d. ( )f x is concave down on ( )5, �.e. As 0 , ( )x f x  f. As , ( ) 0x f x  1 -4 -3 -2 -1 1 2 3 4 5 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 f g1.1 GROUP EXERCISES 3. a. Graph by hand 4 if 1( ) 0 if 12 5 if 1x xf x xx x    .b. State the domain and range of f.4. Find the domain of each function. Give a complete explanation to support your answer.a. ( )2f x x= +b.( )21g xx x=-2-4 -3 -2 -1 1 2 3 4 5-4-3-2-112345671.1 COMPUTER INSTRUCTIONS INTRODUCTION TO GRAPHING WITH CONVERGEIn 1.1 GROUP EXERCISES problem 4 (Example 7, p. 17 in your text), you were asked to find the domain of the functions a. f x x( )   2 and b. g xx x( ) 12. From an algebraic analysis, we see that the domain of f x x( )   2 is x  2 and the domain of g xx x( ) 12 is x x x 0 1,m r. We will now use Converge to graph these functions and verify their domains.First, we will use Converge to graph f x x( )   2. Choose Graph, then Graph Without a File (or simply click on ), choose Y =F(X), and specify 1 function. Click on Next or hit ENTER. Type the function: click on then type( x + 2 ) then hit ENTER. Use this window: Note: Use the TAB key to move from one choice to the next. Min X: 3, MaxX: 3, Min Y: 2, Max Y: 3. Then hit ENTER.Sketch the graph here:How does the graph of f x x( )   2 verify that the domain is x  2 ?Next, graph g xx x( ) 12. Again, click on (Graph Without a File), choose Y = F(X), and specify 1 function and hit ENTER. Type the function: 1 / (x^2  x) and hit ENTER. Use this window: Min X: 3, Max X: 3, Min Y: 10, Max Y: 10. Then hit ENTER.Sketch the graph here:31.1 COMPUTER EXAMPLES How does the graph of g xx x( ) 12 verify that the domain is all real numbers except 0and 1 ?A Piecewise Defined Function: This example investigates the piecewise defined function f xx x xx x( )   RST22 12 1 1 if if . To graph a piecewise function in Converge, the first function is enclosed in parentheses, followed by a FOR statement in brackets, then a semicolon, then the second function in parentheses followed by its FOR statement in brackets.Click on , choose Y =F(X), and specify 1 function and hit ENTER. Type the function as follows: (x^2 2 x) [ for x < =1 ] ; (2x  1) [ for x > 1] and hit ENTER.Use this window: Min X: –3, Max X: 3, Min Y: –2, Max Y: 9. Hit ENTER to accept the remaining settings. Do you believe this is the correct graph? Why or why not?Graph the function again. Click on (re-graph) right below the graph. Press ENTER to accept the function. When you get to the window, look for the option “Min distance for graph break checking”. Notice that the default value is 9R. This has to do with the number of rows on the screen and it is easier to work with actual units. What Converge will do is connect plotted points unless it finds vertical breaks that are a specified distance apart. Converge needs to be given some guidance on a vertical distance that would indicate a break in the graph. A good rule of thumb is to specify a distance that is half of the actual vertical break distance. Notice that this graph has a vertical break of 1 unit. Click in this box and type .5 and then hit ENTER.Was the break displayed properly this time?Before we leave this function, try one other option. Once again, Click on to re-graph the function and press ENTER to accept the function. This time look for the option “Enhance break points”. Click in this box and then hit ENTER.What has changed about the graph?41.1 COMPUTER INSTRUCTIONS 51.2 COMPUTER EXAMPLES SECTION 1.2: MATHEMATICAL MODELSPolynomial Functions: Verify the graph of y x x x  4 23 in Figure 8(b) on page 30.Click on , choose Y =F(X), and specify 1 function and hit ENTER. Type the function as follows: x^4  3x^2 + x and hit ENTER. Use this window: Min X: –4, Max X: 4, MinY: –6, Max Y: 6. If the Min distance for graph break checking is still set at .5 from the previous example, reset it to 9R, and if Enhance break points is checked, click again in this box to turn it off. Then hit ENTERHow many zeros could a polynomial of degree 4 have?How many zeros does this polynomial, y x x x  4 23, have?One of the zeros is obvious – what is it?Write down your estimate of approximate values for each of the remaining zeros.Using Converge to estimate zeros of a function:Suppose we use Converge to obtain more accurate approximations to the zeros. Choose Post-graph, then Estimate Function Zeros. Type in your estimate for the left-most zero and hit ENTER and Converge will give you its best estimate. Continue to type in your estimates to get the remaining zeros. Write all the zeros here:How many turning points (relative extrema) could a polynomial of degree 4 have? How many relative extrema does this polynomial have? Using Converge to estimate the coordinates of the relative extrema of a function:We can …