To determine the equation described in the table using function notation, we can observe the values of \( x \) and \( y \) to identify a pattern.
The values in the table are:
\[ \begin{align*} y & = -10 \quad \text{when} \quad x = 0 \ y & = -9 \quad \text{when} \quad x = 1 \ y & = -8 \quad \text{when} \quad x = 2 \ y & = -7 \quad \text{when} \quad x = 3 \ \end{align*} \]
From the observations:
- As \( x \) increases by 1, \( y \) increases by 1.
This indicates a linear relationship with the slope \( m = 1 \).
We also know that when \( x = 0 \), \( y = -10 \). This gives us the \( y \)-intercept \( b = -10 \).
Therefore, we can write the equation in the slope-intercept form \( y = mx + b \) as follows:
\[ y = 1x - 10 \]
In function notation:
\[ f(x) = 1x - 10 \]
Thus, filling in the blanks:
\[ f(x) = 1x + (-10) \]
So, the final answer is:
\[ f(x) = 1x - 10 \]
You can summarize as:
- The coefficient of \( x \) is 1.
- The constant is -10.