To determine which equation matches the given table, we can substitute the x-values from the table into each equation and check if the resulting y-values match the given values.
Let's go through each equation and see which one matches the given table:
1. F(x) = 2x - 1:
- For x = 0: F(0) = 2(0) - 1 = -1 (not 1)
- For x = 2: F(2) = 2(2) - 1 = 3 (not 5)
- For x = 5: F(5) = 2(5) - 1 = 9 (not 26)
- For x = 7: F(7) = 2(7) - 1 = 13 (not 50)
2. F(x) = 2x + 1:
- For x = 0: F(0) = 2(0) + 1 = 1 (matches)
- For x = 2: F(2) = 2(2) + 1 = 5 (matches)
- For x = 5: F(5) = 2(5) + 1 = 11 (not 26)
- For x = 7: F(7) = 2(7) + 1 = 15 (not 50)
3. F(x) = x² + 1:
- For x = 0: F(0) = (0)² + 1 = 1 (matches)
- For x = 2: F(2) = (2)² + 1 = 5 (matches)
- For x = 5: F(5) = (5)² + 1 = 26 (matches)
- For x = 7: F(7) = (7)² + 1 = 50 (matches)
4. F(x) = x² - 1:
- For x = 0: F(0) = (0)² - 1 = -1 (not 1)
- For x = 2: F(2) = (2)² - 1 = 3 (not 5)
- For x = 5: F(5) = (5)² - 1 = 24 (not 26)
- For x = 7: F(7) = (7)² - 1 = 48 (not 50)
From the analysis above, we can see that the equation F(x) = x² + 1 is the one that matches the given table, as it produces the corresponding y-values for each given x-value.