Question

Two tables were generated to compare the functions f(x) and g(x)=f(x)−1. Find the missing value in the table for the function g(x).(1 point)
 

x f(x)
0 0
−1 1
2 4
x g(x)
0 −1
−1
2 3

Answer 1

To find the missing value in the table for the function \( g(x) = f(x) - 1 \), we first need to use the values given in the table for \( f(x) \).

Here are the steps:

1. When \( x = 0 \):
\[
f(0) = 0
\]
Therefore,
\[
g(0) = f(0) - 1 = 0 - 1 = -1
\]

2. Next, for \( x = -1 \):
\[
f(-1) = 1
\]
Thus,
\[
g(-1) = f(-1) - 1 = 1 - 1 = 0
\]

3. Finally, when \( x = 2 \):
\[
f(2) = 4
\]
Therefore,
\[
g(2) = f(2) - 1 = 4 - 1 = 3
\]

Now, we can summarize the values for \( g(x) \):

- For \( x = 0 \): \( g(0) = -1 \)
- For \( x = -1 \): \( g(-1) = 0 \)
- For \( x = 2 \): \( g(2) = 3 \)

Thus, the missing value for \( g(-1) \) is **0**.

So the completed table for \( g(x) \) is:

\[
\begin{align*}
x & \quad g(x) \\
0 & \quad -1 \\
-1 & \quad 0 \\
2 & \quad 3 \\
\end{align*}
\]

The missing value is **0**.