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Chapter 2 Section 2: Graphs of Equations in Two Variables

Chapter 2 Section 2: Graphs of Equations in Two Variables. In this section, we will… Determine if a given ordered pair satisfies a graph Find the intercepts of a graph of a function algebraically and graphically Identify symmetries given a graph or equation.

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Chapter 2 Section 2: Graphs of Equations in Two Variables

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  1. Chapter 2 Section 2: Graphs of Equations in Two Variables • In this section, we will… • Determine if a given ordered pair satisfies a graph • Find the intercepts of a graph of a function algebraically and graphically • Identify symmetries given a graph or equation

  2. Example:Determine if the given points are on the graph of the equation. 2.2 Determine if a Given Ordered Pair Satisfies a Graph

  3. The graph of an equation in two variables x and y consist of the set of points on the xy-plane whose coordinates satisfy the equation. • Finding x- and y-intercepts: • (algebraically and on the TI) • x-intercept • y-intercept 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically

  4. Example:Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept y-intercept 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically

  5. Example:Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept y-intercept 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically

  6. Example:Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept(s) y-intercept 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically

  7. Example:Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept(s) y-intercept 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically

  8. A graph is said to be symmetric with respect to the x-axis if, for every point (x, y) on the graph, the point (x, -y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the x-axis. If you replace y with –y in the equation and an equivalent equation results, the graph is symmetric with respect to the x-axis. 2.2 Identify Symmetries Given a Graph or Equation

  9. A graph is said to be symmetric with respect to the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the y-axis. If you replace x with –x in the equation and an equivalent equation results, the graph is symmetric with respect to the y-axis. 2.2 Identify Symmetries Given a Graph or Equation

  10. A graph is said to be symmetric with respect to the origin if, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the origin. If you replace x with –x and y with –y in the equation and an equivalent equation results, the graph is symmetric with respect to the origin. 2.2 Identify Symmetries Given a Graph or Equation

  11. Example:For each of the graphs below, find the intercepts and indicate if the graph is symmetric with respect to the x-axis, the y-axis or the origin. x-intercept(s): y-intercept(s): symmetries: x-intercept(s): y-intercept(s): symmetries: 2.2 Identify Symmetries Given a Graph or Equation

  12. Example:For each of the graphs below, find the intercepts and indicate if the graph is symmetric with respect to the x-axis, the y-axis or the origin. x-intercept(s): y-intercept(s): symmetries: x-intercept(s): y-intercept(s): symmetries: 2.2 Identify Symmetries Given a Graph or Equation

  13. Example:Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axis y-axis origin 2.2 Identify Symmetries Given a Graph or Equation

  14. Example:Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axis y-axis origin 2.2 Identify Symmetries Given a Graph or Equation

  15. Example:Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axis y-axis origin 2.2 Identify Symmetries Given a Graph or Equation

  16. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 163-171 Homework: pp. 171-173 #11, 13, 17-23 odds, 29-33 odds, 39-65 odds 2.2 Graphs of Equations in Two Variables

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