To compare the functions \( f(x) \) and \( g(x) \) as provided in the table, we'll list the values of \( f(x) \) and \( g(x) \) at the specified points and then determine when \( f(x) \) is greater than \( g(x) \).
Given values from the table:
- When \( x = -2 \): \( f(x) = -1 \), \( g(x) = -1 \)
- When \( x = -1 \): \( f(x) = -1 \), \( g(x) = 0 \)
- When \( x = 0 \): \( f(x) = 0 \), \( g(x) = 1 \)
- When \( x = 1 \): \( f(x) = 1 \), \( g(x) = 1 \)
- When \( x = 2 \): \( f(x) = 2 \), \( g(x) = 3 \)
- When \( x = 3 \): \( f(x) = 3 \), \( g(x) = 3 \)
Now we can compare the values:
- \( x = -2 \): \( f(-2) = -1 \), \( g(-2) = -1 \) → \( f(-2) = g(-2) \)
- \( x = -1 \): \( f(-1) = -1 \), \( g(-1) = 0 \) → \( f(-1) < g(-1) \)
- \( x = 0 \): \( f(0) = 0 \), \( g(0) = 1 \) → \( f(0) < g(0) \)
- \( x = 1 \): \( f(1) = 1 \), \( g(1) = 1 \) → \( f(1) = g(1) \)
- \( x = 2 \): \( f(2) = 2 \), \( g(2) = 3 \) → \( f(2) < g(2) \)
- \( x = 3 \): \( f(3) = 3 \), \( g(3) = 3 \) → \( f(3) = g(3) \)
From this comparison, we see that \( f(x) \) is not greater than \( g(x) \) for any of the listed values. Therefore, the conclusion is:
\( f(x) > g(x) \) for no values of \( x \) in the provided table.
1 answer