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

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

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

f(x)=−5x−4

Answer 1

To find the equation that describes the function using function notation, let's look at the pairs of \(x\) and \(y\) provided:

\[
\begin{align*}
x=0 & \quad y=-5 \\
x=1 & \quad y=-9 \\
x=2 & \quad y=-13 \\
x=3 & \quad y=-17 \\
\end{align*}
\]

The changes in \(y\) as \(x\) increases can help us find the slope of the function.

Calculating the differences in \(y\):

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

The slope \(m\) is \(-4\).

Now, we can use the slope-intercept form of a linear equation, which is:

\[
y = mx + b
\]

Substituting \(m = -4\):

\[
y = -4x + b
\]

To find \(b\), we can use one of the points in the table. Using the point \((0, -5)\):

\[
-5 = -4(0) + b \implies b = -5
\]

Now, the equation is:

\[
y = -4x - 5
\]

In function notation, it is expressed as:

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

Thus, the correct answer is:

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