Choose the function that represents the data in the table
The Correct Answer and Explanation is:
The correct function that represents the data in the table is y = 3x² + 2.
To determine the correct function, we can systematically test each multiple choice option using the data points from the table. The goal is to find the one equation that holds true for every (x, y) pair.
Let’s start with the first data point, where x = 1 and y = 5.
- Option 1: y = 3x + 2. Substituting x=1, we get y = 3(1) + 2 = 5. This matches, so this option is a possibility.
- Option 2: y = 3x² + 2. Substituting x=1, we get y = 3(1)² + 2 = 3 + 2 = 5. This also matches, so it remains a possibility.
- Option 3: y = x/3 + 2. Substituting x=1, we get y = 1/3 + 2 = 2.33. This does not equal 5, so we can eliminate this option.
- Option 4: y = 3^x + 2. Substituting x=1, we get y = 3¹ + 2 = 5. This matches, so this option is also a possibility.
Now, let’s use the second data point, where x = 2 and y = 14, to test the remaining three options.
- Option 1: y = 3x + 2. Substituting x=2, we get y = 3(2) + 2 = 6 + 2 = 8. This does not equal 14, so this option is incorrect.
- Option 2: y = 3x² + 2. Substituting x=2, we get y = 3(2)² + 2 = 3(4) + 2 = 12 + 2 = 14. This matches the table.
- Option 4: y = 3^x + 2. Substituting x=2, we get y = 3² + 2 = 9 + 2 = 11. This does not equal 14, so this option is also incorrect.
After testing the first two points, only the function y = 3x² + 2 remains. We can verify this with another point, such as x=3 and y=29. For this function, y = 3(3)² + 2 = 3(9) + 2 = 27 + 2 = 29. This is a perfect match. A final check with x=5 and y=77 gives y = 3(5)² + 2 = 3(25) + 2 = 75 + 2 = 77. This confirms that the function correctly represents all the data in the table.
