Graphs of Basic Polynomial Functions
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1 Section 1 2A: Graphs of Basic Polynomial Functions The are nine Basic Functions that we learn to graph in this chapter. The pages that follow this page will show how several values can be put into the function and the related y values found. This process will give several ordered pairs to plot as points on a graph. After plotting several points a general shape for each function can then be determined. The requirement for this chapter is that you will memorize the basic shape for each the following 9 basic functions. Plotting points is discouraged. For this reason no scale is provided on the and y ais. The graph of y = The graph of y = 2 The graph of y = 3 The graph of y = 3 The graph y = The graph of y = 1 The graph of y = 1 2 The graph of y = The graph of y = [ ] y Math 400 Section 1 2A Page Eitel
2 The graph y = 1. Domain: can be any real number so the domain of the function is all real numbers. Range: y can be any real number greater than or equal to 0. y 0 2. The intercept is at (0, 0 ) The y intercept is at (0, 0 ) 3. The point ( 0, 0 ) is the point where the graph changes from decreasing to increasing. This point is called the verte point for the graph. The graph of y = 2 1. Domain: can be any real number so the domain of the function is all real numbers. Range: y can be any real number greater than or equal to The intercept is at (0, 0 ) The y intercept is at (0, 0 ) 3. The point ( 0, 0 ) is the point where the graph changes from decreasing to increasing. This point is called the verte point for the graph. Math 400 Section 1 2A Page Eitel
3 The Graph of y = 3 1. Both the Domain and Range of the function is all real numbers. 2. The intercept is at (0, 0 ) The y intercept is at (0, 0 ) 3. The point ( 0, 0 ) is the point where the graph has a change in it. This point is called the verte point for the graph. The graph y = 1. Domain: can be any real number greater than or equal to 0. 0 Range: y can be any real number greater than or equal to 0. y 0 2. The intercept is at (0, 0 ) The y intercept is at (0, 0 ) 3. The point ( 0, 0 ) is the point where the graph starts. This point is called the verte point for the graph. Math 400 Section 1 2A Page Eitel
4 The graph of 3 1. Both the Domain and Range of the function is all real numbers. 2. The intercept is at (0, 0 ) The y intercept is at (0, 0 ) 3. The point ( 0, 0 ) is the point where the graph has a change in it. This point is called the verte point for the graph. The graph of y = 1 1. Domain: can be any real number ecept 0. Range: y can be any real number ecept There are no or y intercepts. 3. The ais is a horizontal asymptote. We use a dotted line to show the asymptotic line. 4. The y ais is a vertical asymptote. We use a dotted line to show the asymptotic line. Math 400 Section 1 2A Page Eitel
5 The graph of y = Domain: can be any real number ecept 0. Range: y can be any real number ecept There are no or y intercepts. 3. The ais is a horizontal asymptote. We use a dotted line to show the asymptotic line. 4. The y ais is a vertical asymptote. We use a dotted line to show the asymptotic line. The graph of y = y 1. Domain: can be any real number ecept 0. Range: y is 1 or There are no or y intercepts. Math 400 Section 1 2A Page Eitel
6 The functiony = [ ] is called the Greatest Integer Function It is also called the step function due to the graph of the function. The graph of y = [ ] We will select several positive values for and find the related y values y = [ ] says the y value for any value is the greatest integer LESS THAN OR EQUAL to f () = 0 for all on the interval [ 0,1) The greatest integer less than or equal to 0.00 is 0. ( 0.0, 0 ) The greatest integer less than or equal to 0.25 is 0 ( 0.23, 0 ) The greatest integer less than or equal to 0.45 is 0 ( 0.45, 0 ) The greatest integer less than or equal to 0.67 is 0. ( 0.67, 0 ) f () = 1 for all on the interval [ 1,2) The greatest integer less than or equal to 1.00 is 1 ( 1.00, 1 ) The greatest integer less than or equal to 1.17 is 1 ( 1.17, 1 ) The greatest integer less than or equal to 1.39 is 1 ( 1.39, 1 ) The greatest integer less than or equal to 1.82 is 1 ( 1.82, 1 ) f () = 2 for all on the interval [ 2,3) The greatest integer less than or equal to 2.00 is 2 ( 2.00, 2 ) The greatest integer less than or equal to 2.35 is 2 ( 2.35, 2 ) The greatest integer less than or equal to 2.54 is 2 ( 2.54, 2 ) The greatest integer less than or equal to 2.91 is 2 ( 2.91, 2 ) Math 400 Section 1 2A Page Eitel
7 We will select several negative values for and find the related y values The graph of y = [ ] y = [ ] says that the y value for any value is the greatest integer less than or equal to () = 1 for all on the interval [ 1, 0 ) The greatest integer less than or equal to 0.13 is 1. ( 0.13, 1 ) The greatest integer less than or equal to 0.25 is 1 ( 0.25, 1 ) The greatest integer less than or equal to 0.45 is 1 ( 0.45, 1 ) The greatest integer less than or equal to 1.00 is 1 ( 1.00, 1 ) f () = 2 for all on the interval [ 2, 1 ) The greatest integer less than or equal to 1.13 is 1. ( 1.13, 2 ) The greatest integer less than or equal to 1.25 is 1 ( 1.23, 2 ) The greatest integer less than or equal to 1.45 is 1 ( 1.45, 2 ) The greatest integer less than or equal to 2.00 is 1 ( 2.00, 2 ) f () = 2 for all on the interval [ 3, 2 ) The greatest integer less than or equal to 2.13 is 2 ( 2.13, 3 ) The greatest integer less than or equal to 2.25 is 2 ( 2.25, 3) The greatest integer less than or equal to 2.45 is 2 ( 2.45, 3 ) The greatest integer less than or equal to 3.00 is 2 ( 3.00, 3 ) 1. Domain: can be any real number. Range: y can be any Integer. 2. The only or y intercepts is ( 0, 0). Math 400 Section 1 2A Page Eitel
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