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Identifying Linear or Nonlinear Functions: Tables, Graphs, Equations

Learn to identify linear or nonlinear functions using tables, graphs, and equations with examples and explanations. Understand rate of change and determine function types.

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Identifying Linear or Nonlinear Functions: Tables, Graphs, Equations

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 9) Main Idea and Vocabulary Example 1: Identify Functions Using Tables Example 2: Identify Functions Using Tables Example 3: Identify Functions Using Graphs Example 4: Identify Functions Using Graphs Example 5: Identify Functions Using Equations Example 6: Identify Functions Using Equations Example 7: Real-World Example Lesson Menu

  3. Determine whether a function is linear or nonlinear. • nonlinear function Main Idea/Vocabulary

  4. Identify Functions Using Tables Determine whether the table represents a linear or nonlinear function. Explain. As x increases by 2, y increases by a greater amount each time. Answer: The rate of change is not constant, so this function is nonlinear. Example 1

  5. A B C D Determine whether the table represents a linear or nonlinear function. Explain. A. Linear; rate of change is not constant. B. Linear; rate of change is constant. C. Nonlinear; rate of change is not constant. D. Nonlinear; rate of change is constant. Example 1

  6. Identify Functions Using Tables Determine whether the table represents a linear or nonlinear function. Explain. As x increases by 3, y increases by 9 each time. Answer: The rate of change is constant, so this function is linear. Example 2

  7. A B C D Determine whether the table represents a linear or nonlinear function. Explain. A. Linear; rate of change is not constant. B. Linear; rate of change is constant. C. Nonlinear; rate of change is not constant. D. Nonlinear; rate of change is constant. Example 2

  8. Identify Functions Using Graphs Determine whether the graph represents a linear or nonlinear function. Explain. Answer: The graph is a curve, not a straight line. So it represents a nonlinear function. Example 3

  9. A B C D Determine whether the table represents a linear or nonlinear function. Explain. A. Nonlinear; graph is a straight line. B. Nonlinear; graph is a curve. C. Linear; graph is a straight line. D. Linear; graph is a curve. Example 3

  10. Identify Functions Using Graphs Determine whether the graph represents a linear or nonlinear function. Explain. Answer: The graph is a straight line, so the rate of change is constant. The graph represents a linear function. Example 4

  11. A B C D Determine whether the table represents a linear or nonlinear function. Explain. A. Nonlinear; graph is a straight line. B. Nonlinear; graph is a curve. C. Linear; graph is a straight line. D. Linear; graph is a curve. Example 4

  12. Identify Functions Using Equations Determine whether y = 5x2 + 3 represents a linear or nonlinear function. Explain. Since the power of x is greater than 1, this function is nonlinear. Answer: Nonlinear; since x is raised to the second power, the equation cannot be written in the form y = mx + b. Example 5

  13. A B C D Determine whether y = x2 – 1 represents a linear or nonlinear function. Explain. A. linear; is written in the form y = 2x3 – 1 B. Linear; power of x is greater than 1. C. nonlinear; is written in the form y = 2x3 – 1 D. Nonlinear; power of x is greater than 1. Example 5

  14. Identify Functions Using Equations Determine whether y – 4 = 5x represents a linear or nonlinear function. Explain. Rewrite the equation as y = 5x + 4. Answer: Since the equation can be written in the form y = mx + b, this function is linear. Example 6

  15. A B C D Determine whether –3x = y + 6 represents a linear or nonlinear function. Explain. A. linear; can be written in the form y = 3x + 6 B. linear; can be written in the form y = –3x – 6 C. nonlinear; can be written in the form y = 3x + 6 D. nonlinear; can be written in the form y = –3x – 6 Example 6

  16. CLOCKS Use the table below to determine whether or not the number of revolutions per hour that the second hand on a clock makes is a linear function of the number of hours that pass. Examine the difference between the second hand revolutions for each hour. 120 – 60 = 60180 – 120 = 60240 – 180 = 60300 – 240 = 60 Answer: The differences are the same, so the function is linear. Example 7

  17. A B GEOMETRY Use the table below to determine whether or not the sum of the measures of the angles in a polygon is a linear function of the number of sides. A. linear B. nonlinear Example 7

  18. End of the Lesson End of the Lesson

  19. Five-Minute Check (over Chapter 9) Image Bank Math Tools Area Models of Polynomials Multiplying and Dividing Monomials Resources

  20. A B C D (over Chapter 9) Find f(3) if f(x) = 4x – 10. A. 22 B. 2 C. –2 D. –22 Five Minute Check 1

  21. A B C D (over Chapter 9) Find the slope of the line that passes through the points (5, 2) and (1, –2). A. –7 B. –1 C. 1 D. 7 Five Minute Check 2

  22. A B C D (over Chapter 9) Find the slope and y-intercept of y = 3x – 2. A. –3; 2 B. –2; 3 C. 2; 3 D. 3; –2 Five Minute Check 3

  23. A B C D (over Chapter 9) James has 38 stamps in his stamp collection. He collects about 6 stamps a month. How many stamps will James have in 7 months? A. 80 B. 51 C. 42 D. 13 Five Minute Check 4

  24. A B C D (over Chapter 9) Refer to the table. What is the value of f(x) when x = 4? A. –6 B. –5 C. 6 D. 7 Five Minute Check 5

  25. End of Custom Shows

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