Question

Use the table to answer the question.

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

Answer 1

To find the equation described in the table, let's examine the values of \(x\) and \(y\):

The table shows the following pairs of \((x, y)\):

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

From the observations, we can see a pattern.

If we analyze the changes to \(y\) as \(x\) increases:
- As \(x\) increases by 1, \(y\) increases by 1 as well.
- This suggests that \(y\) is a linear function of \(x\).

We can express \(y\) as:
\[
y = x - 10
\]

This can be expressed in function notation as:
\[
f(x) = x - 10
\]

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