Question

Naming, Evaluating, & Interpreting Functions Quick Check
1 of 51 of 5 Items
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(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)=−5x−4
f left parenthesis y right parenthesis equals negative 5 x minus 4
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Answer 1

To determine the equation that describes the function represented in the table, we can analyze the relationship between the values of \(x\) and \(y\):

Given the points in the table:

- \( (0, -5) \)
- \( (1, -9) \)
- \( (2, -13) \)
- \( (3, -17) \)

We can see that as \(x\) increases by 1, \(y\) decreases by 4. This indicates that the relationship is linear.

To find the equation, we can start with the slope \(m\):

\[
m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-5)}{1 - 0} = \frac{-4}{1} = -4
\]

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

\[
y = mx + b
\]

We already have our slope \(m = -4\). To find the y-intercept \(b\), we can use one of the points from the table. Let's use the point \( (0, -5) \):

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

Combining these, we get the equation:

\[
y = -4x - 5
\]

In function notation, this can be expressed as:

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

Thus, the correct response is:

**f(x) = −4x − 5** (first response)