Comparing Shapes of Functions Practice

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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GPT-4o mini · Answer

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 $.