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)
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 \( f(x) \) from the first table and plug them into the equation for \( g(x) \).

Let's do it step by step:

1. For \( x = 0 \):
\[
g(0) = f(0) - 1 = 0 - 1 = -1 \quad \text{(this matches the table)}
\]

2. For \( x = -1 \):
We need to find \( g(-1) \):
\[
g(-1) = f(-1) - 1
\]
From the first table, we see that \( f(-1) = 1 \):
\[
g(-1) = 1 - 1 = 0
\]

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

Now we have completed all entries. The missing value \( g(-1) \) is \( 0 \).

Therefore, the missing value in the table for \( g(x) \) when \( x = -1 \) is:

\[
\boxed{0}
\]