More Concerning Functions and Graphing restart;

Recall that we use the -> (minus greater than) notation to define a function. Suppose we want to enter the function 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 . Suppose, by accident, we forget to enter this as function but instead enter this as an expression. f := x^4+x^3;

NiM+JSJmRywmKiQpJSJ4RyIiJSIiIiIiIiokKSUieEciIiQiIiIiIiI=

Note, since this is an expression, we cannot find f(3) properly. f(3);

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We could simply fix this by reentering the expression as a function or use the unapply command. The unapply command has the form unapply(expression, variable), were expression is converted to a function of the specified variable. To convert the expression f stored above to function of x, we can enter f := unapply(f, x);

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Having f now expressed as a function now allows us to easily do many different types of function evaluations. f(3); simplify(f(x-2)); simplify((f(x+h)-f(x))/h);

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Recall, to unassign f , we can enter f := 'f';

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Maple makes it easy to define the composition of functions. Let 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 and 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. We enter these functions and form f(g(x)) and g(f(x)). f := x->sqrt(x+1); g := x -> x^2-4*x+5;

NiM+JSJmR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2Ii0lJXNxcnRHNiMsJiUieEciIiIiIiIiIiI2IjYiNiI= NiM+JSJnR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwoKiQpJSJ4RyIiIyIiIiIiIiomIiIlIiIiJSJ4RyIiIiEiIiIiJiIiIjYiNiI2Ig==

Now compute the compositions f(g(x)); g(f(x));

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The command that graphs functions in Maple is the plot command. The plot command has the structure plot(expression or function , range , options), where expression or function is the expression or function we want to play, range gives the interval on the x-axis for which the graph will be plotted, and options are specfied parameters that are given to add to the graph in a certain way (more details on this will be given below). To do simple plot of the function 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, we can enter f := x^2-4*x+3;

NiM+JSJmRywoKiQpJSJ4RyIiIyIiIiIiIiomIiIlIiIiJSJ4RyIiIiEiIiIiJCIiIg==

plot(f, x = -2..5);

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In the preceding command, the function in the first parameter was entered as an expression. To plot as a function, we could also enter f := x-> x^2-4*x+3;

NiM+JSJmR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwoKiQpJSJ4RyIiIyIiIiIiIiomIiIlIiIiJSJ4RyIiIiEiIiIiJCIiIjYiNiI2Ig==

plot(f(x), x = -2..5);

LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JDdTNyQkISM/ISIiJCIkXSIhIiI3JCQhMkxMTDMjKj51JT0hIzskIjJzXkFaK2stUSIhIzo3JCQhMm5tIno0M205PCEjOyQiMiMzLT0kXHEpejchIzo3JCQhMk1MJGUvJGZgYyIhIzskIjEmKnkyKHB5NjwiISM5NyQkITJNTCQzSyJvXVQiISM7JCIyWzZ4WS5waTEiISM6NyQkITJsbSJIbjdcbDchIzskIjFNImVuQExNbSohIzo3JCQhMk1MZWtPOW83IiEjOyQiMUctSCMzb3B4KSEjOjckJCExKioqXDdvQ0EkKSohIzskIjE7ZUslSDsnKip5ISM6NyQkITFLTGU5Xz5aJCkhIzskIjFpcExsWmpOcSEjOjckJCEtRGMjR3AnbyEjNyQiMmwlW0VSJD0kPWkhIzs3JCQhMWxtbVQ8SFdgISM7JCIyOjhuKVE3TEJhISM7NyQkITFLTCQzbl9KKyUhIzskIjFNTFIiUTg6dyUhIzo3JCQhMSgqKioqXHNaTFwjISM7JCIxRHd4PXBdZlMhIzo3JCQhMSQqKioqKlxQVnQoKiEjPCQiMlBjRTJOKlsrTSEjOzckJCIxOisrXXMyT1shIzwkIjJqejtWbiYqKTNHISM7NyQkIjJ2bTthRyJINT0hIzwkIjIkKSlRQEpdbDNCISM7NyQkIjFOTExlaiV5USQhIzskIjIvUlZoW08nZjwhIzs3JCQiMm1MTExWVVVzJSEjPCQiMiNRZE4jcChbTDghIzs3JCQiMSwrdm8oKXl5aSEjOyQiMTgiZV93anIjKSkhIzs3JCQiMUxMTCRvRFtsKCEjOyQiMUwnKSkzKkdMU18hIzs3JCQiMS8rdm9pYmsiKiEjOyQiMlBbM2AzJW9TPCEjPDckJCIyMCtEMW88LTEiISM7JCExazkhPiM+NG82ISM7NyQkIjJQTCQzLSQ9LUAiISM7JCEyY25lanBbQ3ckISM8NyQkIjJPTDN4cGx6TSIhIzskITEpPl1qbzcmW2QhIzs3JCQiMm1tO0goW2EnXCIhIzskITFZXThdJEhgWSghIzs3JCQiMm9tVCZ5bygzbCIhIzskITEsPmpnLzgieSkhIzs3JCQiMi0rREpNQl95IiEjOyQhMSYpZmh3KTQoUSYqISM7NyQkIjFubVQwN0tJPiEjOiQhMVFUJmVsWzkmKiohIzs3JCQiKyZcQC0zIyEiKiQhMV8nKlI8XmtOKiohIzs3JCQiMi8rXVBvcG9BIyEjOyQhMHZeZlksYFsqISM6NyQkIjIxK3ZvTWYob0IhIzskITFFSyM0V2wsaykhIzs3JCQiLURFT0lFRCEjNiQhMS81JypIXC9JcyEjOzckJCIxTExMb1QneW0jISM6JCExZFVjRVhkUmIhIzs3JCQiMSwrXWktLD5HISM6JCEybXonPioqPUEjSCQhIzw3JCQiMmptVCYpM3JmJkghIzskITA2WXN5Rj5oKSEjOzckJCIxLCtdWmFxMEohIzokIjIweTZqT1hlQSMhIzw3JCQiMUwkMy0iUWZZSyEjOiQiMTB0XHc3JypSYiEjOzckJCIyLSt2VnVpUVIkISM7JCIxc2djLE5gRyUqISM7NyQkIjJOTExlL1h5YCQhIzskIjJ0NyUqXFFuXE8iISM7NyQkIjIoKipcKD08ImUpbyQhIzskIjFaMix1aklePSEjOjckJCIxb21td3p2TFEhIzokIjFLJykpcEpvRU8jISM6NyQkIjFubSJ6QUFBKVIhIzokIjJgInAlMydcP0hIISM7NyQkIjFNJDMtN2QlSFQhIzokIjJFKGYhb2koZU1OISM7NyQkIjEsKysmcF1aRSUhIzokIjJ2KUhdNWQ0SFQhIzs3JCQiMU1MZSpSNyk+VyEjOiQiMV5zPFw/XGJbISM6NyQkIjFubW1POV1lWCEjOiQiMSpSRDlnSGZhJiEjOjckJCIudm8oR1AxWiEjNyQiMW1Zb1tUWENqISM6NyQkIjEsXTc4WiF6JVshIzokIjEjZlJdRGgwNighIzo3JCQiI10hIiIkIiMhKSEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUlVklFV0c2JDskISM/ISIiJCIjXSEiIiUoREVGQVVMVEctJStBWEVTTEFCRUxTRzYkUSJ4NiJRITYiLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQk9VTkRTX1lHNiMsJC0lJkZsb2F0RzYjJSlpbmZpbml0eUchIiItJS1CT1VORFNfV0lEVEhHNiMsJC0lJkZsb2F0RzYjJSlpbmZpbml0eUchIiItJS5CT1VORFNfSEVJR0hURzYjLCQtJSZGbG9hdEc2IyUpaW5maW5pdHlHISIiLSUpQ0hJTERSRU5HNiI=

To graph the function in certain ways, we can add more parameters involving options. Here are a few of the options available. These and other options can be see by specifying ? plot[options]. view( x-range, y-range) lets you select the viewing rectangle, like the windows command on a graphing calculator thickness the thickness of the curve (values can be 1, 2, or 3 - default is 1), useful if curve is barely visible in a printout. color color of the curve. If not specified, a default color is chosen by Maple. title title (specified in quotes) of the graph numpoints selecting a large number will increase the resolution of the graph and take out artificial corners If you click on the graph you'll see some additional icons at the top of the screen, which may help to improve the looks of your graph. For the previous function, we can add some these options and the next command illustrates: plot(f(x), x = -1 .. 5, view = [-2..5, -2..6], thickness = 3, color = blue, title = "my parabola");

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

In the previous command, we plotted the function 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 with points specfied over the interval x = -1..5. To view the graph, the x axis ranges from -2 to 5 and the y axis ranges from -2 to 6. The thickness option of 3 gives the graph maximum resolution. The color of the graph is specified to be blue with a title of "my parabola". There are a couple of methods available for graphing multiple curves on the same graph. One method encloses the functions to be plotted within brackets separated by commas. To demonstrate, suppose we desire to plot the function 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 in red with a thickness of 2, along with 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 in blue with a thickness of 1. We plot these functions on the interval 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. The following commands accomplishes this task. f := x -> cos(1/2*Pi*x); g := x -> exp(-x);

NiM+JSJmR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2Ii0lJGNvc0c2IywkKiYjIiIiIiIjIiIiKiYlI1BpRyIiIiUieEciIiIiIiIiIiI2IjYiNiI= NiM+JSJnR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2Ii0lJGV4cEc2IywkJSJ4RyEiIjYiNiI2Ig==

plot([f(x), g(x)], x = -Pi .. 3*Pi, color = [red, blue], thickness = [2, 1]);

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The graphs can be seen more to scale by adding the view parameter with an x axis range from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JC1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZJLUYsNiVRJSZwaTtGJy8lJ2l0YWxpY0dGOkY1Ris= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JI21uR0YkNiRRIjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRJSZwaTtGJy8lJ2l0YWxpY0dGPkY1Ris= and y axis range from -5 to 5, as the next command demonstrates. plot([f(x), g(x)], x = -Pi .. 3*Pi, view = [-Pi..3*Pi, -5..5], color = [red, blue], thickness = [2, 1]);

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Another method for plotting the graph involves storing each separate graph plots as variables and displaying them together. This feature especially convenient when one wants to graph functions over different intervals on the x axis. To demonstrate, suppose we enter the following two functions: f := x -> x^2; 1; g := x -> x^5;

NiM+JSJmR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiokKSUieEciIiMiIiI2IjYiNiI= NiMiIiI= NiM+JSJnR2YqNiMlInhHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiokKSUieEciIiYiIiI2IjYiNiI=

The following commands set up and store the plots for these graphs in the variables p1 and p2. NOTE!! An important fact to remember is to end thesecommands with a colon : . If you end the command with a semicolon, all the data points generated to plot the graph will be displayed. p1 := plot(f(x), x = -3 .. 3, color = blue): p2 := plot(g(x), x = -1.2 .. 1.2, color = black, thickness = 2): Note the different interval values for x that are specified. To plot the two graphs, we must specify a command in the Maple plots package. The plots package is not available as a standard part of Maple and must be read in. This can be done with the following statement with(plots);

Warning, the name changecoords has been redefined 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

The output of the preceding statement gives all the new commands that we now have available to use. The one we need is the display command. To display the plots stored in p1 and p2, we enter display([p1, p2], view = [-4 .. 4, -5 .. 10], title = "f(x) = x^2 and g(x) = x^5 with different intervals");

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

Note in the preceding display command that the same options, such as view and title, can be specified like we did in the plot command.

1. Using the unapply command, convert the assignment to a function and compute 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. > f := tan(x) + sec(x); 2. Determine f(g(x)) and g(f(x)) for the following functions. a. 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 and 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. b. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiUtRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEieEYnRjZGOUZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGXG8tRiM2JS1GLDYlUSdhcmNzaW5GJy9GN0ZERkBGPC1GVzYkLUYjNiVGKy1GIzYjLUklbXN1cEdGJDYlRmVuLUkjbW5HRiQ2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQEYrRis= and 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 3. Using the plot command, graph the following functions a. 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 b. 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. Note this function can be created by entering g := x->exp(sin(x)); 4. Using the plot command, plot the following functions on the same graph. Color one function red with a thickness of 2 and the other blue with a thickness of 1. Create a title for your graph. a. 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 and 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 . . b. 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 and 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. . 5. By storing your plots and using the display command, plot the graph of 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 on the interval -2 <= x <= 2 and the graph of 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 on the interval 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 <= x <= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRJSZwaTtGJy8lJ2l0YWxpY0dGPkY1Ris= .