Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 36 | Quadratic Functions in Tabular and Graph Form: Example 36TopicQuadratics DescriptionIn this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. It demonstrates the role of the quadratic terms in determining the graph's curvature and the significance of intercepts in solving quadratic equations. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 37 | Quadratic Functions in Tabular and Graph Form: Example 37TopicQuadratics DescriptionIn this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows a downwardly opening parabola that has two roots, one of them shown in the table. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 4 | Quadratic Functions in Tabular and Graph Form: Example 4TopicQuadratics |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 5 | Quadratic Functions in Tabular and Graph Form: Example 5TopicQuadratics DescriptionThis example provides a quadratic function displayed in both tabular and graphical forms. The table lists values that, when plotted, create a parabolic curve on the graph. This visual representation helps in identifying key features such as the vertex, axis of symmetry, and roots. By analyzing these features, students can understand the impact of different coefficients on the shape and position of the parabola. Skills involved include interpreting data from tables, graphing functions, and understanding the vertex and standard forms of quadratic equations. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 6 | Quadratic Functions in Tabular and Graph Form: Example 6TopicQuadratics DescriptionIn this example, a quadratic function is presented through both tabular and graphical forms. The accompanying image provides a visual interpretation of the function, emphasizing the relationship between the x-values and their corresponding y-values. This representation allows learners to recognize the nature of quadratic functions, particularly how changes to the function parameters affect the shape and position of the graph. The skills required include critical graph analysis, understanding symmetry in parabolas, and solving for x-intercepts. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 7 | Quadratic Functions in Tabular and Graph Form: Example 7TopicQuadratics DescriptionA detailed view of a quadratic function is depicted here, where the data table and graph work in conjunction to showcase the solution process for the function. Analyzing this illustration aids in comprehending how the quadratic function applies to specific scenarios and enhances one’s ability to derive equations from graphs. Such comparative analysis of multiple representations bolsters problem-solving skills and equips students with the tools to tackle different forms of quadratic equations. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 8 | Quadratic Functions in Tabular and Graph Form: Example 8TopicQuadratics DescriptionThis image presents a quadratic function in tabular and graphic format. The graph reflects the nature of parabolic functions, while the table reinforces the numerical data needed for graphing. By exploring both representations, students can appreciate the convergence of algebra and geometry, honing their capacity for critical thinking and analysis. Understanding the properties of the parabola is essential for mastery in quadratic equations by applying skills such as completing the square or using the quadratic formula. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Quadratics--Quadratic Functions in Tabular and Graph Form: Example 9 | Quadratic Functions in Tabular and Graph Form: Example 9TopicQuadratics DescriptionThis example consolidates the properties of quadratic functions by using a table to present values and a graph to illustrate their relationship. The significance of identifying intercepts, the vertex, and axis of symmetry becomes apparent when viewed together. Mastering these concepts through multiple formats allows for invaluable preparation for advanced algebraic topics, thereby enhancing overall mathematical comprehension and problem-solving abilities. |
Graphs of Quadratic Functions and Quadratic Equations and Functions | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / x. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with branches in the first and third quadrants, illustrating the characteristic shape of this basic rational function. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 10 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 10TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = -1 / (x - 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph includes labeled points at certain coordinates, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 11 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 11TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x - 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph is plotted with labeled points at given coordinates, illustrating how the negative sign and constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 12 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 12TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1). The image presents both the table of x-y coordinates and the resulting graph. The graph includes points labeled at specified coordinates, demonstrating how the negative signs in both the numerator and denominator, along with the constant, affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 13 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 13TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1) + 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The table contains specific x-y coordinates: (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), (2, 1.333), which are plotted on the graph. This example illustrates how adding a constant to a rational function affects its graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 14 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 14TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x + 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, -2), (-1.5, -3), (0, 0), (1.5, -0.6), (2, -0.667), which are plotted on the graph. This example illustrates how subtracting a constant from a rational function affects its graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 15 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 15TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (x + 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, 2), (-1.5, 3), (0, 0), (1.5, 0.6), (2, 0.667), which are plotted on the graph. This example demonstrates how negating the numerator of a rational function and adding a constant affects its graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 16 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 16TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = -1 / (x + 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The table contains specific x-y coordinates: (-2, 0), (-1.5, 1), (0, -2), (1.5, -1.4), (2, -1.333), which are plotted on the graph. This example illustrates how negating the numerator of a rational function and subtracting a constant affects its graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 17 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 17TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x + 1) + 1. The image showcases both the table of x-y coordinates and the resulting graph. Points plotted include (-2, 1.333), (-1.5, 1.4), (0, 2), (1.5, -1), and (2, 0). The graph features a hyperbola with asymptotes, illustrating how negating the x-term in the denominator and adding a constant affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 18 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 18TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x + 1) - 1. The image presents both the table of x-y coordinates and the resulting graph. Points plotted include (-2, -0.667), (-1.5, -0.6), (0, 0), (1.5, -3), and (2, -2). The graph shows a hyperbola with vertical and horizontal shifts, demonstrating how negating the x-term in the denominator and subtracting a constant affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 19 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 19TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x - 1) + 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. Points include (-2, 0.667), (-1.5, 0.6), (0, 0), (1.5, 3), and (2, 2). The graph is a hyperbola with asymptotes at x = 1 and y = 1, illustrating how subtracting a constant in the denominator and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 2 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 2TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / x. The image showcases both the table of x-y coordinates and the resulting graph. The graph is a hyperbola with branches in the second and fourth quadrants, illustrating how the negative sign affects the function's shape compared to the previous example. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 20 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 20TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x - 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, -1.333), (-1.5, -1.4), (0, -2), (1.5, 1), and (2, 0). The graph is a hyperbola with shifted asymptotes at x = 1 and y = -1, illustrating how subtracting a constant in the denominator and from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 21 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 21TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = (-1) / (-x + 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. It includes a table of x-y coordinates: (-2, 0.667), (-1.5, 0.6), (0, 0), (1.5, 3), and (2, 2). The graph is plotted on a grid, demonstrating how negating both the numerator and x-term in the denominator, while adding a constant to the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 22 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 22TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = (-1) / (-x + 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. It includes a table of x-y coordinates: (-2, -1.333), (-1.5, -1.4), (0, -2), (1.5, 1), and (2, 0). The graph is plotted on a grid, illustrating how negating both the numerator and x-term in the denominator, while subtracting a constant from the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 23 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 23TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = (-1) / (x - 1) + 1. The image shows both a table of x-y coordinates and the corresponding graph. The table includes points such as (-2, 1.333), (-1.5, 1.4), (0, 2), (1.5, -1), and (2, 0). The graph is plotted on a grid, illustrating how subtracting a constant in the denominator and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 24 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 24TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = (-1) / (x - 1) - 1. The image shows both a table of x-y coordinates and the corresponding graph. The table includes points such as (-2, -0.667), (-1.5, -0.6), (0, 0), (1.5, -3), and (2, -2). The graph is plotted on a grid, illustrating how subtracting constants both in the denominator and from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 25 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 25TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x - 1) + 1. The image showcases both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, 2), (-1.5, 3), (0, 0), (1.5, 0.6), and (2, 0.667), illustrating how negating both terms inside the parentheses and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x - 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph shows points plotted at (-2, 0), (-1.5, 1), (0, -2), (1.5, -1.4), and (2, -1.333), illustrating how negating both terms inside the parentheses and subtracting a constant from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), and (2, 1.333), demonstrating how negating both the numerator and the terms inside the parentheses, while adding a constant to the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, -2), (-1.5, -3), (0, 0), (1.5, -0.6), and (2, -0.667), illustrating how negating both the numerator and the terms inside the parentheses, while subtracting a constant from the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x). The image presents both the table of x-y coordinates and the resulting graph. Interestingly, the graph is identical to that of y = -1 / x, showing a hyperbola with branches in the second and fourth quadrants. This example demonstrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x). The image showcases both the table of x-y coordinates and the resulting graph. Notably, the graph is identical to that of y = 1 / x, displaying a hyperbola with branches in the first and third quadrants. This example further illustrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with points marked at specific coordinates, illustrating how the addition of a constant in the denominator affects the graph's position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (x + 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph displays a hyperbola with labeled points on the curve, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with specific points highlighted, illustrating how the negative sign and constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x - 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph features a hyperbola with marked points on its curve, illustrating how the constant in the denominator affects the graph's position. |
Rational Functions and Equations | |
Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x + 1). The image presents both the table of x-y coordinates and the resulting graph. The graph is plotted with points labeled at specific coordinates, demonstrating how the negative signs in both the numerator and denominator affect the graph's shape and position. |
Rational Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 1 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 1TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 10 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 10TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 11 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 11TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 12 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 12TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 13 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 13TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 14 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 14TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 15 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 15TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 16 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 16TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 17 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 17TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 18 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 18TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 19 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 19TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 2 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 2TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 20 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 20TopicSpecial Functions |
Polynomial Functions and Equations | |
Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 21 | Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 21TopicSpecial Functions |
Polynomial Functions and Equations |