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# 5.1 Linear Functions And Graphs

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### 5.1 Linear Functions And Graphs

1. 1. 5.1 Linear Functions and Graphs Student Study Guide
2. 2. Definitions <ul><li>Domain: first coordinates in a set of ordered pairs, x values </li></ul><ul><li>(3, 4), (5, 6) - Domain = 3, 5 </li></ul><ul><li>Range: second coordinates in a set of ordered pairs, y values </li></ul><ul><li>(3, 4), (5, 6) - Range = 4, 6 </li></ul><ul><li>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 </li></ul>
3. 3. Exercises: Determine the domain and range of each relation. <ul><li>5. (2, 9), (3, 10), (5, 12), (9, 14) </li></ul>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. 4. Exercises: Determine whether each relation is a function <ul><li>1. (12, 7), (6, 5), (12, -7), (6, -5) </li></ul><ul><li>When two x values are the same, it is NOT a function. </li></ul><ul><li>Domain: 12 and 12 </li></ul><ul><li>Use the vertical line test to see if it is a function </li></ul>
5. 5. Exercises: Determine whether each relation is a function <ul><li>3. (1, 3), (2, 3), (4 ,3), (5 ,3) (6, 3) </li></ul><ul><li>When two y values are the same, it IS a function. </li></ul><ul><li>Range: 3 </li></ul><ul><li>Use the vertical line test to see if it is a function </li></ul>
6. 6. 5.1 Linear Functions and Graphs Practice Masters Level B
7. 7. For each relation, (a) describe the domain, (b) describe the range, and (c), determine whether the relation is a function <ul><li>1. (8, 12.5), (10, 12.3), (15, 12.1) </li></ul>a. Domain: 8, 10, 15 b. Range: 12.5, 12.3, 12.1 c. Function
8. 8. Complete each ordered pair so that it is a solution to 2x - y = 10 <ul><li>(2, ___ ) </li></ul><ul><li>(___, 8) </li></ul><ul><li>(-1, ___) </li></ul>
9. 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. <ul><li>Every 3 pictures increases 30 cents </li></ul><ul><li>Every 1 picture increases 10 cents </li></ul><ul><li>\$2.00 processing fee </li></ul>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. 10. Write a set of ordered pairs for the function. <ul><li>(12, 3.20) </li></ul>(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. 11. Identify the domain shown in the table. <ul><li>12, 15, 24, 36 </li></ul>Number of pictures, x 12 15 24 36 Cost, in dollars, y \$3.20 \$3.50 \$4.40 \$5.60
12. 12. 12. Identify the range shown in the table. <ul><li>3.20, 3.50, 4.40, 5.60 </li></ul>Number of pictures, x 12 15 24 36 Cost, in dollars, y \$3.20 \$3.50 \$4.40 \$5.60
13. 13. 13. The graph below shows a linear function. Complete the table of values, and determine an equation of the line. <ul><li>Y = 2x + 1 </li></ul>X Y 0 1 2 3 X Y 0 1 1 3 2 5 3 7