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(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
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Answer 1

To determine the correct function that describes the relationship between \( x \) and \( y \) in the given table, we can first analyze the values:

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

We can see that as \( x \) increases, \( y \) decreases. Let's find the difference in the \( y \)-values as \( x \) increases by 1:

- From \( x = 0 \) to \( x = 1 \): \( -9 - (-5) = -4 \)
- From \( x = 1 \) to \( x = 2 \): \( -13 - (-9) = -4 \)
- From \( x = 2 \) to \( x = 3 \): \( -17 - (-13) = -4 \)

The \( y \)-values decrease by 4 each time \( x \) increases by 1.

Thus, we can infer that the function has a slope of -4, which leads us to consider a linear function of the form \( y = mx + b \).

Now, let's find the intercept \( b \) when \( x = 0 \):
- When \( x = 0 \), \( y = -5 \), so \( b = -5 \).

Thus, the equation can be written as:
\[
y = -4x - 5
\]

In function notation, this can be expressed as:
\[
f(x) = -4x - 5
\]

Out of the given options, the correct equation that describes the function in the table is:
**f(x)=−4x−5**.