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Exploring Algebra: Functions, Tables, and Graphs

Learn about function rules, tables, and graphs in Algebra 1 Lesson 8-6,7. Practice modeling functions, creating tables of values, and graphing data.

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Exploring Algebra: Functions, Tables, and Graphs

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  1. 1. 2. 3. xy –3 –7 –1 –1 0 2 2 8 xy –4 –3 0 –2 2 –1.5 4 –1 xy –3 4 –2 0 0 –2 2 4 Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 (For help, go to Lesson 5-2.) Graph the data in each table. 8-6,7

  2. 3. Graph the points: (–4, –3) (0, –2) (2, –1.5) (4, –1) Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 1. Graph the points: 2. Graph the points: (–3, –7) (–3, 4) (–1, –1) (–2, 0) (0, 2) (0, –2) (2, 8) (2, 4) Solutions 8-6,7

  3. Model the function rule y = + 2 using a table of values and a graph. Step 1:Choose input value for x. Evaluate to find y Step 2: Plot the points for the ordered pairs. Step 3: Join the points to form a line. x (x, y) –3y = (–3) + 2 = 1 (–3, 1) 0y = (0) + 2 = 2 (0, 2) 3y = (3) + 2 = 3 (3, 3) 1 3 1 3 x y = x + 2 1 3 1 3 1 3 Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 8-6,7

  4. vC(v) = 5 + 3v (v, C(v)) 0C(0) = 5 + 3(0) = 5 (0, 5) 1C(1) = 5 + 3(1) = 8 (1, 8) 2C(2) = 5 + 3(2) = 11 (2, 11) Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 At the local video store you can rent a video game for $3. It costs you $5 a month to operate your video game player. The total monthly cost C(v) depends on the number of video games v you rent. Use the function rule C(v) = 5 + 3v to make a table of values and a graph. 8-6,7

  5. Make a table of values. Then graph the data. xy = |x| + 2 (x, y) –3 y = |–3| + 2 = 5 (–3, 5) –1 y = |–1| + 2 = 3 (–1, 3)   0 y = |0| + 2 = 2 (0, 2)   1 y = |1| + 2 = 3 (1, 3) 3 y = |3| + 2 = 5 (3, 5) Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 a. Graph the function y = |x| + 2. 8-6,7

  6. Make a table of values. Then graph the data. x ƒ(x) = x2 + 2 (x, y) –2 ƒ(–2) = 4 + 2 = 6 (–2, 6) –1 ƒ(–1) = 1 + 2 = 3 (–1, 3) 0 ƒ(0) = 0 + 2 = 2 ( 0, 2) 1 ƒ(1) = 1 + 2 = 3 ( 1, 3) 2 ƒ(2) = 4 + 2 = 6 ( 2, 6) Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 (continued) b. Graph the function ƒ(x) = x2 + 2. 8-6,7

  7. xy = –2x + 4 (x, y) –1 y = –2(–1) + 4 = 6 (–1, 6) 0 y = –2(0) + 4 = 4 (0, 4) 1 y = –2(1) + 4 = 2 (1, 2) 2 y = –2(2) + 4 = 0 (2, 0) Function Rules, Tables, and Graphs ALGEBRA 1 LESSON 8-6,7 1. Model y = –2x + 4 with a table of values and a graph. 2. Graph y = |x| – 2. 3. Graph ƒ(x) = 2x2 – 2. 8-6,7

  8. Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 (For help, go to Lesson 8-6,7.) Model each rule with a table of values. 1.f(x) = 5x – 1 2.y = –3x + 4 3.g(t) = 0.2t – 7 4.y = 4x + 1 5.f(x) = 6 – x6.c(d) = d + 0.9 Evaluate each function rule for n = 2. 7.A(n) = 2n – 1 8.f(n) = –3 + n – 1 9.g(n) = 6 – n 8-6,7

  9. 3. 4. 2. 5. 1. 6. Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 Solutions 8-6,7

  10. Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 Solutions (continued) 7.A(n) = 2n – 1 for n = 2: A(2) = 2(2) – 1 = 4 – 1 = 3 8.f(n) = –3 + n – 1 for n = 2: f(2) = –3 + 2 – 1 = –1 – 1 = –2 9.g(n) = 6 – n for n = 2: g(2) = 6 – 2 = 4 8-6,7

  11. a. x ƒ(x) 2 8 4 10 6 12 8 14 Relate:    equals plus 6 Write: = + 6 ƒ(x) x ƒ(x) x Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 Write a function rule for each table. Ask yourself, “What can I do to 2 to get 8, 4 to get 10, ...?” You add 6 to each x-value to get the ƒ(x) value. A rule for the function is ƒ(x) = x + 6. 8-6,7

  12. xy 1 2 2 5 3 10 4 17 Relate:    equals plus 1 Write: = + 1 y x times itself y x2 Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 (continued) b. Ask yourself, “What can I do to 1 to get 2, 2 to get 5, . . . ?” You multiply each x-value times itself and add 1 to get the y value. A rule for the function is y = x2 + 1. 8-6,7

  13. money earned number of pages sold Relate:    is  25  times   n Define: Let = number of pages sold. P(n) Let = money earned. P(n) n Write: = 25 • Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 The journalism class makes $25 per page of advertising in the yearbook. If the class sells n pages, how much money will it earn? a. Write a function rule to describe this relationship. The function rule P(n) = 25n describes the relationship between the number of pages sold and the money earned. 8-6,7

  14. Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 (continued) b. The class sold 6 pages of advertising. How much money did the class make? P(6) = 25 • 6 Substitute 6 for n. P(6) = 150 Simplify. P(n) = 25 • n The class made $150. 8-6,7

  15. total profit tapes sold Relate: is $5.50 times minus cost of tape production t Define: Let = number of tapes sold. P(t) Let = total profit. P(t) t Write: = 5.5 • – 100 Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 The choir spent $100 producing audio tapes of its last performance and will sell the tapes for $5.50 each. Write a rule to describe the choir’s profit as a function of the number of tapes sold. The function rule P(t) = 5.5t – 100 describes the profit as a function of the number of tapes sold. 8-6,7

  16. x ƒ(x) –1 –4 0 –3 1 –2 2 –1 xy –1 –5 0 0 1 5 2 10 b. a. Writing a Function Rule ALGEBRA 1 LESSON 8-6,7 1. Write a function rule for each table. y = 5x ƒ(x) = x – 3 2. Write a function rule to describe each relationship. a. the total cost T(c) of c pounds of apples at $.82 a pound b. a scale model s of a moth m that is 6 times the actual size of the moth T(c) = 0.82c s(m) = 6m 3. You borrow $60 to buy a bread-making machine. You charge customers $1.50 a loaf for your special bread. Write a rule to describe your profit as a function of the number n of loaves sold. P(n) = 1.5n - 60 8-6,7

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