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

Let's fill in the missing information from the table for \( f(x) \):

1. For \( x = 0 \):
- \( f(0) = 0 \)
- Therefore, \( g(0) = f(0) - 1 = 0 - 1 = -1 \) (this is already provided).

2. For \( x = -1 \):
- We have \( g(-1) \) and need to find \( f(-1) \).
- According to the table for \( g(x) \), it is provided that \( g(-1) = 2 \).
- Thus, from the relationship \( g(x) = f(x) - 1 \), we have:
\[
2 = f(-1) - 1
\]
- Therefore, solving for \( f(-1) \):
\[
f(-1) = 2 + 1 = 3
\]

3. For \( x = 1 \):
- According to the table for \( f(x) \), it is provided that \( f(1) = 1 \).
- Thus, we can calculate \( g(1) \):
\[
g(1) = f(1) - 1 = 1 - 1 = 0
\]

4. For \( x = 2 \):
- It is provided that \( f(2) = 4 \).
- Thus, we can calculate \( g(2) \):
\[
g(2) = f(2) - 1 = 4 - 1 = 3
\]

After analyzing all the provided information, the missing value for \( g(-1) \) is \( 2 \) since we have that \( g(-1) \) was not given, but it corresponds to \( f(-1) \) being calculated as \( 3 \).

Therefore, the complete entries now are:

- From \( f(x) \):
- \( f(-1) = 3 \)

And from \( g(x) \):
- \( g(-1) = 2 \)

Thus, the missing value in the table for the function \( g(x) \) is \( 2 \).