To determine the equation that describes the function represented in the table, we can analyze the relationship between the values of \(x\) and \(y\):
Given the points in the table:
- \( (0, -5) \)
- \( (1, -9) \)
- \( (2, -13) \)
- \( (3, -17) \)
We can see that as \(x\) increases by 1, \(y\) decreases by 4. This indicates that the relationship is linear.
To find the equation, we can start with the slope \(m\):
\[ m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-5)}{1 - 0} = \frac{-4}{1} = -4 \]
Next, we can use the slope-intercept form of a linear equation, which is:
\[ y = mx + b \]
We already have our slope \(m = -4\). To find the y-intercept \(b\), we can use one of the points from the table. Let's use the point \( (0, -5) \):
\[ y = -4(0) + b \implies -5 = b \]
Combining these, we get the equation:
\[ y = -4x - 5 \]
In function notation, this can be expressed as:
\[ f(x) = -4x - 5 \]
Thus, the correct response is:
f(x) = −4x − 5 (first response)