Question

COmpare the function f(x) and g(x) when is f greater than g

-2,-1,-1
-1, 3/4, 0
0,1,1
1, 1 1/4, 2

Answer 1

To compare the functions \( f(x) \) and \( g(x) \), we need to identify the values of \( f(x) \) and \( g(x) \) from the given coordinates and then find when \( f(x) > g(x) \).

Based on the information you've provided, I assume that the first column corresponds to the values of \( x \), the second column corresponds to \( f(x) \), and the third column corresponds to \( g(x) \). Here's the table of values you've given:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & -1 & -1 \\
-1 & \frac{3}{4} & 0 \\
0 & 1 & 1 \\
1 & \frac{5}{4} & 2 \\
\hline
\end{array}
\]

Now, let's compare the values of \( f(x) \) and \( g(x) \):

- For \( x = -2 \):
- \( f(-2) = -1 \)
- \( g(-2) = -1 \)
- \( f(-2) \) is **not greater than** \( g(-2) \).

- For \( x = -1 \):
- \( f(-1) = \frac{3}{4} \)
- \( g(-1) = 0 \)
- \( f(-1) \) is **greater than** \( g(-1) \).

- For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)
- \( f(0) \) is **not greater than** \( g(0) \).

- For \( x = 1 \):
- \( f(1) = \frac{5}{4} \)
- \( g(1) = 2 \)
- \( f(1) \) is **not greater than** \( g(1) \).

### Summary
\( f(x) > g(x) \) only occurs for \( x = -1 \). For all other values provided (\( x = -2, 0, 1 \)), \( f(x) \) is **not greater than** \( g(x) \).