Use the table to answer the question.

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.