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 need to use the values of \( f(x) \) given in the first table and apply the definition of \( g(x) \).

Let's list the known values from the tables and perform the calculations for \( g(x) \):

### For \( f(x) \):
Given that:
- When \( x = 0 \), \( f(0) = 0 \)
- When \( x = -1 \), \( f(-1) = 1 \)
- When \( x = 2 \), \( f(2) = 4 \)

### Now, calculating \( g(x) = f(x) - 1 \):
1. For \( x = 0 \):
\[
g(0) = f(0) - 1 = 0 - 1 = -1 \quad \text{(matching the table)}
\]

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

3. For \( x = 2 \):
\[
g(2) = f(2) - 1 = 4 - 1 = 3 \quad \text{(matching the table)}
\]

### The missing value for \( g(x) \) when \( x = -1 \) is:
\[
g(-1) = 0
\]

Therefore, the tables should look like this:

### Summary:
- \( x \) | \( f(x) \) | \( g(x) \)
- 0 | 0 | -1
- -1 | 1 | 0 (missing value)
- 2 | 4 | 3

The missing value for \( g(x) \) is **0**.