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 values in the function \( g(x) = f(x) - 1 \), we can use the values of \( f(x) \) provided in the first table:

### Given table for \( f(x) \):

- At \( x = 0 \), \( f(0) = 0 \)
- At \( x = 1 \), the value is missing.
- At \( x = 2 \), \( f(2) = 4 \)

### Filling the table for \( g(x) \):

Using the definition of \( g(x) \):

1. For \( x = 0 \):
\[
g(0) = f(0) - 1 = 0 - 1 = -1
\]

2. For \( x = 1 \):
We need to find \( f(1) \) to compute \( g(1) \).
- The table states that at \( x = 1 \), the corresponding value for \( g(1) \) is missing in the \( g(x) \) table.

3. For \( x = 2 \):
\[
g(2) = f(2) - 1 = 4 - 1 = 3
\]

Now we can analyze the information we have in \( g(x) \):

### Given table for \( g(x) \):

- At \( x = 0 \), \( g(0) = -1 \)
- At \( x = 1 \), the value is missing.
- At \( x = 2 \), \( g(2) = 3 \)

### Finding \( f(1) \) and subsequently \( g(1) \):

We don't have \( f(1) \) in the given data. However, we can compute \( g(1) \):
\[
g(1) = f(1) - 1
\]

Since we don't have \( f(1) \) directly, we cannot determine \( g(1) \) without additional information about \( f(1) \).

Therefore, if we assume \( f(1) \) based on potential positions or patterns, for example:
1. Assuming \( f(1) = 2 \), we can compute:
\[
g(1) = f(1) - 1 = 2 - 1 = 1
\]

**Thus, the missing value at \( x = 1 \) in the \( g(x) \) table is 1.**

Final answer:
- \( g(1) = 1 \)

If \( f(1) \) is different, then the value of \( g(1) \) will change accordingly. Please verify \( f(1) \) to confirm the exact missing value.