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1.7. An Introduction to Functions

1.7. An Introduction to Functions. Goal 1: Input-Output Tables. A function is a rule that establishes a relationship between two quantities, called the input and the output . Input-Output Tables. For each input, there is exactly one output.

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1.7. An Introduction to Functions

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  1. 1.7. An Introduction to Functions

  2. Goal 1: Input-Output Tables A function is a rule that establishes a relationship between two quantities, called the input and the output.

  3. Input-Output Tables • For each input, there is exactly one output. 2. More than one input can have the same output. 0 3 1 1 3 4 2

  4. Input-Output Table One way to describe a function is to make an input-output table.

  5. Input-Output Tables Domain: The collection of all input values Range: The collection of all output values

  6. Making an Input-Output Table 2 1 3 Here are 5 triangles: • Make an input-output table in which the input is the Figure Number and the output is the Triangle Number. • Does the table represent a function? 3. Describe Domain and Range. 4 5

  7. Using a Table to Graph a Function You are at an altitude of 250 feet in a hot-air balloon. You turn on the burner and rise at a rate of 20 feet per minute for 5 minutes. Your altitude h after you have risen for t minutes is given by the function. h = 250 + 20t

  8. Step 1 For several inputs t, use the function to calculate an output h. Example: t = 1 h = 250 + 20(1) h = 250 + 20 h = 270

  9. Step 2 Organize the Data input an input-output table.

  10. Step 3 Graph the data in the table. 300 Altitude (h) 200 100 Time (t)

  11. Step 4 What is the domain of the function? What part of the domain is shown in the table?

  12. Describing a Function We have illustrated that functions can be described in these ways: • Input-Output Table • Description in Words • Equation • Graph

  13. Complete the Sentence A function is a relationship between two quantities, called the __________ and the _________.

  14. Complete the Sentence A function is a relationship between two quantities, called the Input and the Output.

  15. Complete the Sentence. The collection of all input values is the ____________.

  16. Complete the Sentence. The collection of all input values is the domain.

  17. Complete the Sentence. The collection of all output values is the _________ of the function.

  18. Complete the Sentence. The collection of all output values is the range of the function.

  19. Complete the Sentence Four ways to represent a function are • ____________________________ • ____________________________ • ____________________________ • ____________________________

  20. Complete the Sentence Four ways to represent a function are (1) Input-Output Table (2) Words (3) Equation (4) Graph

  21. Does the Table Represent a function?

  22. Does the Table Represent a function? Yes; for each input, there is exactly one output.

  23. Does the Table Represent a function?

  24. Does the Table Represent a function? Yes; for each input, there is exactly 1 output.

  25. Does the Table Represent a function?

  26. Does the Table Represent a function? No; there are 2 output values that correspond to the input value 1.

  27. Make an input-output table for the function. Use 0, 1, 2, and 3 as the domain. y = 3x + 2

  28. Make an input-output table for the function. Use 0, 1, 2, and 3 as the domain. y = 3x + 2 Output: 2, 5, 8, 11

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