Determine the Equation from the Table: Function Matching Challenge

To solve this problem, follow these steps:

• Step 1: Analyze the pattern of the given table. Notice that the increase in $Y$ for each increase of 2 in $X$ is 2, indicating a slope of 1.
• Step 2: Choose a likely linear equation from the provided options.
• Step 3: Verify which equation accurately represents all the data points.

Let's verify the equation $y = x + 1$ with all pairs:

• For $X = -3$, calculate $Y = (-3) + 1 = -2$. This matches the $Y$-value in the table.
• For $X = -1$, calculate $Y = (-1) + 1 = 0$. This too matches the $Y$-value.
• For $X = 1$, calculate $Y = 1 + 1 = 2$. Again, this matches.
• For $X = 3$, calculate $Y = 3 + 1 = 4$. This matches as well.
• For $X = 5$, calculate $Y = 5 + 1 = 6$. Finally, this matches too.

Each of the calculated $Y$-values using $y = x + 1$ aligns with the respective $Y$-values from the table.

Therefore, the correct equation that represents the function is $y = x + 1$.