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

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

f(y)=−5x−4

Answer 1

To find the correct function that describes the relationship in the table, we first need to identify the pattern.

The values in the table are:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -5 \\
1 & -9 \\
2 & -13 \\
3 & -17 \\
\hline
\end{array}
\]

Let's look at the change in \(y\) values as \(x\) increases:

- From \(x=0\) to \(x=1\): \(y\) changes from \(-5\) to \(-9\) (change of \(-4\))
- From \(x=1\) to \(x=2\): \(y\) changes from \(-9\) to \(-13\) (change of \(-4\))
- From \(x=2\) to \(x=3\): \(y\) changes from \(-13\) to \(-17\) (change of \(-4\))

The \(y\) value decreases by 4 for each increase of 1 in \(x\). This suggests a linear function with a slope of -4.

Now, let's find the equation in the form \(y = mx + b\):
1. The slope (\(m\)) is -4.
2. We can use one of the points to find \(b\). Using the point \(x = 0, y = -5\):
\[
-5 = -4(0) + b \implies b = -5
\]

So, the equation is:
\[
y = -4x - 5
\]

In function notation, this is:
\[
f(x) = -4x - 5
\]

Now let's review the answer choices:

1. \(f(x) = -5x - 4\) (incorrect)
2. \(f(x) = -4x - 5\) (correct)
3. \(f(y) = -4x - 5\) (incorrect - should be \(f(x)\))
4. \(f(y) = -5x - 4\) (incorrect - should be \(f(x)\))

Therefore, the correct response is:

**f(x) = -4x - 5.**