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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. Example:Find the intercepts and graph of using a table of values. The y-intercept is where x = 0, and the x-intercept is where y = 0. Label the intercepts. x y 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(s) 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. 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

  8. 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

  9. 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

  10. 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

  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: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

  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

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