Question

Use the table to answer the question.

x y
0 −5
1 −9
2 −13
3 −17
Which of the following equations correctly describes the function in the table using function notation?



(1 point)
Responses

f(x)=−5x−4

f of x is equal to negative 5 x minus 4

f(y)=−5x−4
f left parenthesis y right parenthesis equals negative 5 x minus 4

f(y)=−4x−5
f left parenthesis y right parenthesis equals negative 4 x minus 5

f(x)=−4x−5

Answer 1

To find the correct function, we need to observe the relationship between \(x\) and \(y\) in the table:

- When \(x = 0\), \(y = -5\)
- When \(x = 1\), \(y = -9\)
- When \(x = 2\), \(y = -13\)
- When \(x = 3\), \(y = -17\)

Let's check how \(y\) changes with respect to \(x\):

1. From \(x = 0\) to \(x = 1\), \(y\) changes from \(-5\) to \(-9\). This is a decrease of \(4\) units.
2. From \(x = 1\) to \(x = 2\), \(y\) changes from \(-9\) to \(-13\). Again, this is a decrease of \(4\) units.
3. From \(x = 2\) to \(x = 3\), \(y\) changes from \(-13\) to \(-17\). Once again, this is a decrease of \(4\) units.

This indicates a linear relationship with a consistent change of \(-4\) in \(y\) for each increase of \(1\) in \(x\).

Next, we can write the equation of the line in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

The slope \(m = -4\), and we know that when \(x = 0\), \(y = -5\) (which is the y-intercept). Therefore, we can substitute \(m\) and \(b\) into the equation:

\[y = -4x - 5\]

Using function notation, we express this as:

\[f(x) = -4x - 5\]

Thus, the correct response that describes the function in the table using function notation is:

**f(x)=−4x−5**.