Identify the function and the table structure.

The function is $Y = 4 + 3x - x^2$. The table requires calculating values for 4, $3x$, $-x^2$, and $Y$ for $x$ values from $-1$ to 5.

The previous response was cut off while calculating for $x=0$.
For $x = 0$:

• For $x = 1$:

  $$Y = 4 + 3(1) - (1)^2$$ $$Y = 4 + 3 - 1$$ $$Y = 6$$

• For $x = 2$:

  $$Y = 4 + 3(2) - (2)^2$$ $$Y = 4 + 6 - 4$$ $$Y = 6$$

• For $x = 3$:

  $$Y = 4 + 3(3) - (3)^2$$ $$Y = 4 + 9 - 9$$ $$Y = 4$$

• For $x = 4$:

  $$Y = 4 + 3(4) - (4)^2$$ $$Y = 4 + 12 - 16$$ $$Y = 0$$

• For $x = 5$:

  $$Y = 4 + 3(5) - (5)^2$$ $$Y = 4 + 15 - 25$$ $$Y = -6$$

The table is completed by calculating 4, $3x$, $-x^2$, and $Y = 4 + 3x - x^2$ for each $x$ value.

The completed table is: