Question

Use the table to answer the question.

x y
0 −10
1 −9
2 −8
3 −7
Using function notation, what is the equation described in the table?(1 point)
f(x)=
x+
Remaining Attempts : 3
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Answer 1

To find the function \( f(x) \) that corresponds to the values in the table, we can observe the relationship between \( x \) and \( y \).

The table shows:

- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)

We can see that as \( x \) increases by 1, \( y \) increases by 1. This indicates a linear relationship.

To express this relationship in function notation:

1. The change in \( y \) is \( +1 \) for each increase in \( x \), which suggests a slope of \( 1 \).
2. We can start with the slope-intercept form of a line, \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Given that the function increases by 1 for each increase in \( x \) and starts from \( y = -10 \) when \( x = 0 \), we can derive the equation as follows:

Starting from the point \( (0, -10) \):

- The slope \( m = 1 \)
- The y-intercept \( b = -10 \)

Thus, the equation is:

\[
f(x) = 1x - 10
\]

We can simplify this to:

\[
f(x) = x - 10
\]

So the answer is:

\[
f(x) = x - 10
\]