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Linear Functions: Graphing and Evaluation

Learn how to identify, evaluate, and graph linear functions, and find x-intercepts and y-intercepts. Includes examples and practice problems.

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Linear Functions: Graphing and Evaluation

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  1. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  2. Transparency 2a

  3. 22. no 26. D = {3,4,5,6} R = {3.4.5.6} yes it’s a function 34. D = {x|x ≥ 3} R = all real #’s not a function 42. {(1987,12);(1989,13); 42. (con’t) (1991,11);(1993,12); (1995,9);(1997,6); (1999,3) 44. yrs. (d); reps. (r) 46. -14 54. 39 CD’s 58. C 64. {m|4<m<6) Answers 2.1 Homework

  4. 2.2 Notes • Linear equation – • graph is always a line • in the form y = mx + b • no variable in the denom. • no var. with an exp. greater than 1 • Standard form – • x and y on same side • no fractions or decimals • x should be positive

  5. Lesson 2 Contents Example 1Identify Linear Functions Example 2Evaluate a Linear Function Example 3Standard Form Example 4Use Intercepts to Graph a Line

  6. State whether is a linear function. Explain. Answer: This is a linear function because it is in the form Example 2-1a

  7. State whether is a linear function. Explain. Example 2-1b Answer: This is not a linear function because x has an exponent other than 1.

  8. State whether is a linear function. Explain. Answer: This is a linear function because it can be written as Example 2-1c

  9. State whether each function is a linear function. Explain. a. b. c. Answer: yes; Example 2-1d Answer: No; x has an exponent other than 1. Answer: No; two variables are multiplied together.

  10. MeteorologyThe linear function can be usedto find the number of degrees Fahrenheit, f (C), that are equivalent to a given number of degrees Celsius, C. On the Celsius scale,normal body temperature is 37C.What is normal body temperature in degrees Fahrenheit? Original function Substitute. Simplify. Example 2-2a Answer: Normal body temperature, in degrees Fahrenheit, is 98.6F.

  11. Example 2-2b Thereare 100 Celsius degrees between the freezing and boilingpoints of water and 180 Fahrenheit degrees betweenthese two points. How many Fahrenheit degrees equal1 Celsius degree? Divide 180 Fahrenheit degrees by 100 Celsius degrees. Answer:1.8F= 1C

  12. MeteorologyThe linear function can be usedto find the distance d(s) in miles from a storm, based on the number of seconds s that it takes to hear thunder after seeinglightning. a. If you hear thunder 10 seconds after seeing lightning, howfar away is the storm? b. If the storm is 3 miles away, how long will it take to hear thunderafter seeing lightning? Example 2-2c Answer: 2 miles Answer: 15 seconds

  13. Write in standard form. Identify A, B, and C. Original equation Subtract 3x from each side. Multiply each side by –1 so that A0. and Answer: Example 2-3a

  14. Write in standard form. Identify A, B, and C. Original equation Subtract 2y from each side. Multiply each side by –3 so that the coefficientsare all integers. and Answer: Example 2-3b

  15. Write in standard form. Identify A, B, and C. Original equation Subtract 4 from each side. Divide each side by 2 so that the coefficients have a GCF of 1. and Answer: Example 2-3c

  16. Write each equation in standard form. Identify A, B, and C. a. b. c. Answer: and Answer: and and Answer: Example 2-3d

  17. Find the x-intercept and the y-intercept of the graph of Then graph theequation. The x-intercept is the value of x when Original equation Substitute 0 for y. Add 4 to each side. Divide each side by –2. Example 2-4a The x-intercept is –2. The graph crosses the x-axis at (–2, 0).

  18. Likewise, the y-intercept is the value of y when Original equation Substitute 0 for x. Add 4 to each side. Example 2-4b The y-intercept is 4. The graph crosses the y-axis at (0, 4).

  19. (0, 4) (–2, 0) Example 2-4c Use the ordered pairs to graph this equation. Answer: The x-intercept is –2, and the y-intercept is 4.

  20. Find the x-intercept and the y-intercept of the graph of Then graph theequation. Answer: The x-intercept is –2, and the y-intercept is 6. Example 2-4d

  21. End of Lesson 2

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