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5.1 Linear Functions And Graphs
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5.1 Linear Functions And Graphs

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  • 1. 5.1 Linear Functions and Graphs Student Study Guide
  • 2. Definitions
    • Domain: first coordinates in a set of ordered pairs, x values
    • (3, 4), (5, 6) - Domain = 3, 5
    • Range: second coordinates in a set of ordered pairs, y values
    • (3, 4), (5, 6) - Range = 4, 6
    • Function: Pairing between two sets of numbers in which each element of the first set is paired with exactly one element of the second set
  • 3. Exercises: Determine the domain and range of each relation.
    • 5. (2, 9), (3, 10), (5, 12), (9, 14)
    Domain: 2, 3, 5, 9 Range: 9, 10, 12, 14 7. (0, 17), (7, -12), (13, 21), (18, 40) Domain: 0, 7, 13, 18 Range: 17, -12, 21, 40 5. ( 2 , 9), ( 3 , 10), ( 5 , 12), ( 9 , 14) 5. (2, 9 ), (3, 10 ), (5, 12 ), (9, 14 )
  • 4. Exercises: Determine whether each relation is a function
    • 1. (12, 7), (6, 5), (12, -7), (6, -5)
    • When two x values are the same, it is NOT a function.
    • Domain: 12 and 12
    • Use the vertical line test to see if it is a function
  • 5. Exercises: Determine whether each relation is a function
    • 3. (1, 3), (2, 3), (4 ,3), (5 ,3) (6, 3)
    • When two y values are the same, it IS a function.
    • Range: 3
    • Use the vertical line test to see if it is a function
  • 6. 5.1 Linear Functions and Graphs Practice Masters Level B
  • 7. For each relation, (a) describe the domain, (b) describe the range, and (c), determine whether the relation is a function
    • 1. (8, 12.5), (10, 12.3), (15, 12.1)
    a. Domain: 8, 10, 15 b. Range: 12.5, 12.3, 12.1 c. Function
  • 8. Complete each ordered pair so that it is a solution to 2x - y = 10
    • (2, ___ )
    • (___, 8)
    • (-1, ___)
  • 9. The table below shows the cost for film developing. A processing fee of $2.00 is charged per roll, and there is an additional fee per picture. 9. Write an equation for the function.
    • Every 3 pictures increases 30 cents
    • Every 1 picture increases 10 cents
    • $2.00 processing fee
    Y = 2 + 0.10x Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60
  • 10. 10. Write a set of ordered pairs for the function.
    • (12, 3.20)
    (15, 3.50) (24, 4.40) (36, 5.60) Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60
  • 11. 11. Identify the domain shown in the table.
    • 12, 15, 24, 36
    Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60
  • 12. 12. Identify the range shown in the table.
    • 3.20, 3.50, 4.40, 5.60
    Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60
  • 13. 13. The graph below shows a linear function. Complete the table of values, and determine an equation of the line.
    • Y = 2x + 1
    X Y 0 1 2 3 X Y 0 1 1 3 2 5 3 7

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