1. Warm-up: Write the inverse of the relation shown by the mapping below -2 3 5 8 0 1 (-1, -2) (-1, 3) (0, 3) (1, 5) (0, 8)

2. Objective: Use an equation to determine the range for a given domain Find yif you know x Lesson 4-4

3. Find the solution set for y = 2x + 3 given the replacement set { (2, 7), (-1, 3), (3, 9) } Example 1 These are possible solutions to the equation. We have to test them to see if they make the equation true. This is similar to what we did in chapter 1, but this time we are plugging in a number for x and y!

4. Find the solution set for y = 2x + 3 given the replacement set { (2, 7), (-1, 3), (3, 9) } Example 1 First, check (2, 7)y = 2x + 3 xy 7 = 2(2) + 3 7 = 4 + 3 7 = 7This is true! (2, 7) IS a solution!

5. Find the solution set for y = 2x + 3 given the replacement set { (2, 7), (-1, 3), (3, 9) } Example 1 Now, check (-1, 3)y = 2x + 3 xy 3 = 2(-1) + 3 3 = -2 + 3 3 = 1This is false! (-1, 3) IS NOT a solution!

6. Find the solution set for y = 2x + 3 given the replacement set { (2, 7), (-1, 3), (3, 9) } Example 1 Last, check (3, 9)y = 2x + 3 xy 9 = 2(3) + 3 9 = 6 + 3 9 = 9This is true! (3, 9) IS a solution! The solution set is all the pairs that worked in the equation: { (2, 7) (3, 9) }

7. Find the solution set for 4x + 2y = 10 given the replacement set { (-1, 7), (3, -1), (0, 5) (4, 3) } Example 2 First, check (-1, 7)4x + 2y = 10 xy 4(-1) + 2(7) = 10 -4 + 14 = 10 10 = 10This is true! (-1, 7) IS a solution!

8. Find the solution set for 4x + 2y = 10 given the replacement set { (-1, 7), (3, -1), (0, 5) (4, 3) } Example 2 Next, check (3, -1)4x + 2y = 10 xy 4(3) + 2(-1) = 10 12 + -2 = 10 10 = 10This is true! (3, -1) IS a solution!

9. Find the solution set for 4x + 2y = 10 given the replacement set { (-1, 7), (3, -1), (0, 5) (4, 3) } Example 2 Now, check (0, 5)4x + 2y = 10 xy 4(0) + 2(5) = 10 0 + 10 = 10 10 = 10This is true! (0, 5) IS a solution!

10. Find the solution set for 4x + 2y = 10 given the replacement set { (-1, 7), (3, -1), (0, 5) (4, 3) } Example 2 Last, check (4, 3)4x + 2y = 10 xy 4(4) + 2(3) = 10 16 + 6 = 10 22 = 10This is false! (4, 3) IS NOT a solution! Solution set: { (-1, 7), (3, -1), (0, 5) }

11. Solve the equation y = 8 – 2x if the domain is {-3, 0, 1} Example 3 Recall…. domain is all the x values In a problem like this, we are being given the x’s and have to find the y’s that go along with them. To do this, we will plug each x into the equation one at a time…. and use the equation to find the y that goes with it.

12. Solve the equation y = 8 – 2x if the domain is {-3, 0, 1} Example 3 The first x is -3.y = 8 – 2x y = 8 – 2(-3) y = 8 – (-6) y = 8 + 6 Plug it into the equation. Remember: order of operations!! y = 14 First solution: (-3, 14)

13. Solve the equation y = 8 – 2x if the domain is {-3, 0, 1} Example 3 The 2 nd x is 0.y = 8 – 2x y = 8 – 2(0) y = 8 – 0 y = 8 Plug it into the equation. 2 nd solution: (0, 8)

14. Solve the equation y = 8 – 2x if the domain is {-3, 0, 1} Example 3 The 3 rd x is 1.y = 8 – 2x y = 8 – 2(1) y = 8 – 2 y = 6 Plug it into the equation. 3 rd solution: (1, 6) Solution set: { (-3, 14), (0, 8), (1,6) }

15. Solve the equation 3x + 2y = 12 if the domain is {-2, 0, 4} Example 4 The first x is -2.3x + 2y = 12 3(-2) + 2y = 12 -6 + 2y = 12 2y = 18 Plug it into the equation. y = 9 Solve for y +6 2 2 First solution: (-2, 9)

16. Solve the equation 3x + 2y = 12 if the domain is {-2, 0, 4} Example 4 The 2 nd x is 0.3x + 2y = 12 3(0) + 2y = 12 0 + 2y = 12 2y = 12 Plug it into the equation. y = 6 Solve for y 2 2 2 nd solution: (0, 6)

17. Solve the equation 3x + 2y = 12 if the domain is {-2, 0, 4} Example 4 The 3 rd x is 4.3x + 2y = 12 3(4) + 2y = 12 12 + 2y = 12 2y = 0 Plug it into the equation. y = 0 Solve for y -12 2 2 3 rd solution: (4, 0) Solution set: { (-2, 9), (0, 6), (4, 0) }

18. Assignment: Lesson 4-4, p. 215 #14, 16, 17, 32, 34, 38 Please show work, but don’t graph solution sets