Question

Comparing Shapes of Functions Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items


Question
Use the table to answer the question.

x f(x)
g(x)

−2
−1
−1

−1
34
0
0 1 1
1 114
2
2 3 3
Compare the functions f(x)
and g(x)
. When is f(x)
greater than g(x)
?

(1 point)
f(x)
is greater than g(x)
when
<x<
.
Remaining Attempts : 3
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Answer 1

To compare the functions \( f(x) \) and \( g(x) \) based on the provided table, we can look at the values at each corresponding \( x \) value:

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & -1 & -1 \\
-1 & 34 & 0 \\
0 & 1 & 1 \\
1 & 114 & 2 \\
2 & 3 & 3 \\
\hline
\end{array}
\]

Now, we'll determine where \( f(x) \) is greater than \( g(x) \):

- At \( x = -2 \): \( f(-2) = -1 \) and \( g(-2) = -1 \) → \( f(-2) \) is not greater.
- At \( x = -1 \): \( f(-1) = 34 \) and \( g(-1) = 0 \) → \( f(-1) \) is greater.
- At \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) → \( f(0) \) is not greater.
- At \( x = 1 \): \( f(1) = 114 \) and \( g(1) = 2 \) → \( f(1) \) is greater.
- At \( x = 2 \): \( f(2) = 3 \) and \( g(2) = 3 \) → \( f(2) \) is not greater.

From this analysis, \( f(x) \) is greater than \( g(x) \) at \( x = -1 \) and \( x = 1 \).

Thus,

\( f(x) \) is greater than \( g(x) \) when \( -1 < x < 1 \).

Therefore, the answer is:

\( f(x) \) is greater than \( g(x) \) when \( -1 < x < 1 \).