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Understanding Functions: Domain, Range, and Graphing Techniques

This lesson focuses on understanding functions, specifically the concepts of domain, range, independent and dependent variables. Students will learn to create input-output tables and graph functions by plotting ordered pairs. Examples such as y = ½x – 3 will be analyzed. Participants will engage in hands-on activities to find equations from tables and graphs, and identify the corresponding domains and ranges. This comprehensive approach prepares students to master key concepts in algebra and function analysis.

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Understanding Functions: Domain, Range, and Graphing Techniques

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  1. Function ________________________ ________________________________ Domain _________________________ Range __________________________ Independent variable_______________ Dependent variable________________ Inputs _________________________ Outputs ________________________ Vocabulary

  2. Examples • What is the domain? Range? Domain ______________________ Range _______________________

  3. p. 7 with a partner • domain: range: • domain: range: • domain: range:

  4. Examples • Given the function y = ½x – 3 with a domain of 2,4,6,8 make a table and identify the range.

  5. p. 8 with a partner 4. range: 5. range:

  6. Writing equations from tables . . . • How do you get the output value with the given input value? • See if that works for each case.

  7. Writing an equation (function rule) by looking at a table . . .

  8. p. 8 with a partner 6. 7.

  9. 1.3 Graphing Functions • Graph the function by first making an input-output table and then plotting the ordered pairs on a graph. • Remember . . . x values are the ________, ________, ________ and y values are the _______, __________, ____________. (3 names for each)

  10. Graph the function . . . y = ½x – 2 Domain: 0,2,4,6

  11. p. 11 #2-5 with a partner 2. 3. 4. 5.

  12. Writing an equation (rule) from a graph . . . • Make an input-output table first and then determine what you do to the input (x) to get the output (y).

  13. Last example! Make a table for the graph and write a rule for the function. Identify the domain and range. Domain ____________________________ Range_____________________________ Equation __________________________

  14. p. 12 with a partner 6. 7. 8. 9.

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