Question

Which function below shows the rule for this table?
Responses

x. y
0 -1
1. 2
2. 7
3. 14
4. 23
A y = 2x² - 1y = 2x² - 1

B y = x² + 2x - 1y = x² + 2x - 1

C y = x² + x - 1y = x² + x - 1

D y = 4x - 1

Answer 1

To find the correct function that describes the relationship between the values of \(x\) and \(y\) in the given table, we can evaluate each function option with the provided \(x\) values to see which one matches the corresponding \(y\) values:

### Table Values:
\[
\begin{align*}
x & : 0, 1, 2, 3, 4 \\
y & : -1, 2, 7, 14, 23 \\
\end{align*}
\]

### Evaluating Each Function Option:

#### Option A: \(y = 2x^2 - 1\)
- For \(x = 0\): \(y = 2(0)^2 - 1 = -1\) (correct)
- For \(x = 1\): \(y = 2(1)^2 - 1 = 1\) (incorrect)
- Since it fails, we can skip further calculations.

#### Option B: \(y = x^2 + 2x - 1\)
- For \(x = 0\): \(y = (0)^2 + 2(0) - 1 = -1\) (correct)
- For \(x = 1\): \(y = (1)^2 + 2(1) - 1 = 2\) (correct)
- For \(x = 2\): \(y = (2)^2 + 2(2) - 1 = 7\) (correct)
- For \(x = 3\): \(y = (3)^2 + 2(3) - 1 = 14\) (correct)
- For \(x = 4\): \(y = (4)^2 + 2(4) - 1 = 23\) (correct)

#### Option C: \(y = x^2 + x - 1\)
- For \(x = 0\): \(y = (0)^2 + (0) - 1 = -1\) (correct)
- For \(x = 1\): \(y = (1)^2 + (1) - 1 = 1\) (incorrect)
- Since it fails, we can skip further calculations.

#### Option D: \(y = 4x - 1\)
- For \(x = 0\): \(y = 4(0) - 1 = -1\) (correct)
- For \(x = 1\): \(y = 4(1) - 1 = 3\) (incorrect)
- Since it fails, we can skip further calculations.

### Conclusion
The correct function that matches all values in the table is:
**B: \(y = x^2 + 2x - 1\)**.