Question

Use the table to answer the question.
X: 0,1,2,3 & Y: -5, -9, -13, -17

Which of the following equations correctly describes the function in the table using function notation?

1. f(x) = -4x - 5
2. f(y) = -5x - 4
3. f(x) = -5x - 4
4. f(y) = -4x - 5

Answer 1

To determine which equation correctly describes the function based on the given values of \( X \) and \( Y \), we can start by identifying the relationship between \( X \) and \( Y \).

From the table:
- When \( X = 0 \), \( Y = -5 \)
- When \( X = 1 \), \( Y = -9 \)
- When \( X = 2 \), \( Y = -13 \)
- When \( X = 3 \), \( Y = -17 \)

We notice that as \( X \) increases by 1, \( Y \) decreases by 4. This suggests a linear relationship.

To find the equation, we can start with the point when \( X = 0 \):
- At \( X = 0 \), \( Y = -5\).

Using the slope \( m = -4 \) (because \( Y \) decreases by 4 units for each increase of 1 unit in \( X \)), the equation of the line in slope-intercept form \( Y = mX + b \) can be formulated:

\[
Y = -4X - 5
\]

We can express this using function notation as:
\[
f(x) = -4x - 5
\]

Now, let's examine the options provided:

1. \( f(x) = -4x - 5 \)
2. \( f(y) = -5x - 4 \)
3. \( f(x) = -5x - 4 \)
4. \( f(y) = -4x - 5 \)

The first option \( f(x) = -4x - 5 \) matches our derived equation exactly.

Therefore, the correct answer is:

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