To approach this problem, let’s analyze the given table step by step.
1. Input Table Analysis:
- The given table lists pairs of values where [tex]\( x \)[/tex] corresponds to [tex]\( f(x) \)[/tex].
- Specifically, the table contains:
- When [tex]\( x = 3 \)[/tex], [tex]\( f(x) = 0.25 \)[/tex]
- When [tex]\( x = 5 \)[/tex], [tex]\( f(x) = 0.5 \)[/tex]
- When [tex]\( x = 7 \)[/tex], [tex]\( f(x) = 1 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( f(x) = 2 \)[/tex]
- When [tex]\( x = 11 \)[/tex], [tex]\( f(x) = 4 \)[/tex]
2. Creation of Lookup Structures:
- From the table, we can create a dictionary for easy lookup of [tex]\( f(x) \)[/tex] given [tex]\( x \)[/tex]:
[tex]\[
\{3: 0.25, 5: 0.5, 7: 1, 9: 2, 11: 4\}
\][/tex]
- We can also extract the lists of [tex]\( x \)[/tex] values and [tex]\( f(x) \)[/tex] values:
[tex]\[
x\_values = [3, 5, 7, 9, 11]
\][/tex]
[tex]\[
f\_x\_values = [0.25, 0.5, 1, 2, 4]
\][/tex]
3. Summary of Results:
- The dictionary mapping [tex]\( x \)[/tex] to [tex]\( f(x) \)[/tex]:
[tex]\[
\{3: 0.25, 5: 0.5, 7: 1, 9: 2, 11: 4\}
\][/tex]
- The list of [tex]\( x \)[/tex] values:
[tex]\[
[3, 5, 7, 9, 11]
\][/tex]
- The list of [tex]\( f(x) \)[/tex] values:
[tex]\[
[0.25, 0.5, 1, 2, 4]
\][/tex]
These steps provide us with the necessary structures to easily look up [tex]\( f(x) \)[/tex] values for any [tex]\( x \)[/tex] provided in the table, and also access the [tex]\( x \)[/tex] values and the corresponding [tex]\( f(x) \)[/tex] values separately.
