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 + ___

Answer 1

To determine the equation described in the table using function notation, we need to observe the values of \( y \) as \( x \) changes:

The table provided is as follows:

\[
\begin{array}{c|c}
x & y \\
\hline
0 & -10 \\
1 & -9 \\
2 & -8 \\
3 & -7 \\
\end{array}
\]

From the table, we can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates that the relationship between \( x \) and \( y \) is linear with a slope of 1.

To find the equation in the form \( f(x) = mx + b \), we start with the slope \( m \):
\[
m = 1
\]

Next, we need to find \( b \), which is the y-intercept. By looking at the table, when \( x = 0 \), \( y = -10 \). Therefore, \( b = -10 \).

Putting this information together, the equation can be expressed as:
\[
f(x) = 1x - 10
\]

Thus, in function notation, the equation described in the table is:
\[
f(x) = 1x - 10
\]

So, filling in the blanks:
\( f (x) = 1x + (-10) \).