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Graphs of Functions Defined by Expressions in a Linear Equation

Chapter 4 Discovery 1. Graphs of Functions Defined by Expressions in a Linear Equation. On a standard screen, graph the following functions, determined from the given linear equation: 1. 2. Describe the characteristic of the graph of the function defined by the expression in Y1.

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Graphs of Functions Defined by Expressions in a Linear Equation

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  1. Chapter 4 Discovery 1 Graphs of Functions Defined by Expressions in a Linear Equation On a standard screen, graph the following functions, determined from the given linear equation: 1. 2. Describe the characteristic of the graph of the function defined by the expression in Y1. Describe the characteristic of the graph of the function defined by the expression in Y2. 1 of 2

  2. Chapter 4 Discovery 1 Graphs of Functions Defined by Expressions in a Linear Equation On an integer screen, graph the following functions, determine from the given nonlinear equation: 3. Describe the characteristic of the graph of the function defined by the expression in Y1. Describe the characteristic of the graph of the function defined by the expression in Y2. 2 of 2

  3. Chapter 4 Discovery 2 Numerical Solutions To solve the equation, , complete the extended table of values shown, compare the values obtained, and determine the difference of the values. x = 0 6 1 2 3 4 Write a rule to determine the solution of an equation from a table of values.

  4. Chapter 4 Discovery 3 Linear Equations with Noninteger Solutions does not have an integer solution. Complete the table of values, compare the values obtained, and determine their differences. Write a rule for determining when the solution of an equation is between two integers given in a table of values.

  5. Chapter 4 Discovery 4 Graphical Solutions To solve the equation , graph the functions and . Label the point of intersection of the graphs. Write a rule for determining the solution of an equation from the graph of the two functions. Write a rule for determining the numeric value of each expression when the equation is evaluated at its solution.

  6. Chapter 4 Discovery 5 Linear Equations with No Solution 1. Solve numerically by completing a table of values. Write a rule explaining how to solve the equation by viewing its table. 2.Solve graphically. Sketch the graph. Write a rule explaining how to solve the equation by viewing its graph.

  7. Chapter 4 Discovery 6 Linear Equation with Many Solutions 1. Solve numerically by completing a table of values. Write a rule explaining how to solve the equation by viewing its table of values. 2. Solve graphically. Sketch the graph. Write a rule explaining how to solve the equation by viewing its graph.

  8. Chapter 4 Discovery 7 Addition Property of Equations Given the equation 7 = 7, add 2 to both expressions. 7 = 7 7 + 2 7 + 2 9 9 1. Given the equation 7 = 7, add -2 to both expressions. 2. Given the equation 6 + 1 = 4 + 3, add 2 to both expressions. 3. Given the equation 6 + 1 = 4 + 3, add -2 to both expressions. Write a rule for the addition property of equations.

  9. Chapter 4 Discovery 8 Multiplication Property of Equations Given the equation 7 = 7, multiply both expressions by 2. 7 = 7 7 • 2 7 • 2 14 14 1. Given the equation 7 = 7, multiply both expressions by -2. 2. Given the equation 6 + 1 = 4 + 3, multiply both expressions by 2. 3. Given the equation 6 + 1 = 4 + 3, multiply both expressions by -2. Write a rule for the multiplication property of equations.

  10. Chapter 4 Discovery 9 Linear Equation with No Solution Solve algebraically the previous example of a linear equation with no solution: Write a rule that explains why the equation has no solution.

  11. Chapter 4 Discovery 10 Linear Equations with Many Solutions Solve algebraically the previous example of a linear equation with many solutions: Write a rule that explains why the equation has many solutions.

  12. Chapter 4 Discovery 11 Graphs of the Function Defined by Expressions in a Linear Absolute-Value Equation On an integer screen, graph the following functions, determined from the given linear absolute-value equation: 1. 2. Explainthe characteristic of the graphs of the functions defined by the absolute-value expression, Y1. Explain the characteristic of the graphs of the functions defined by the constant, Y2. 1 of 2

  13. Chapter 4 Discovery 11 Graphs of the Function Defined by Expressions in a Linear Absolute-Value Equation On an integer screen, graph the following functions, determined from the given linear absolute-value equation: Explain the characteristic of the graphs of the functions defined by the absolute-value expression, Y1. Explain the characteristic of the graphs of the functions defined by the constant, Y2. 2 of 2

  14. Chapter 4 Discovery 12 Solving a Linear Absolute-Value Equation Solve each equation graphically and check your solution numerically. 1. a. b. 2. a. b. 3. a. b. Write a rule for the number of solutions of a linear absolute-value equation when the absolute-value expression equals a positive number, a negative number, and 0.

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