Answer :
To determine whether the relationship represented by the table is a function, we need to check if each input value (x) is associated with exactly one output value (f(x)).
Here’s a step-by-step explanation:
1. Understand the Definition of a Function:
A relationship is a function if and only if every input (x-value) is associated with exactly one output (f(x)-value). This means no x-value should map to more than one f(x)-value.
2. Examine the Table:
Let's look at the table of values provided:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
64.1 & 10 \\
-55.4 & 34.5 \\
-44 & -75.7 \\
64.1 & -73 \\
-55.9 & -97.7 \\
\hline
\end{array}
\][/tex]
3. Identify Duplicate x-Values:
- Notice that the x-value 64.1 appears twice in the table.
- The first time it appears, it maps to an f(x)-value of 10.
- The second time it appears, it maps to an f(x)-value of -73.
4. Check for Multiple Outputs:
- Since the x-value 64.1 is associated with two different f(x)-values (10 and -73), this violates the definition of a function.
5. Conclusion:
- Because there is at least one x-value (64.1) that does not map uniquely to a single f(x)-value, the relationship represented by the table does NOT qualify as a function.
Therefore, the answer is: No, the table does NOT represent a function.
Here’s a step-by-step explanation:
1. Understand the Definition of a Function:
A relationship is a function if and only if every input (x-value) is associated with exactly one output (f(x)-value). This means no x-value should map to more than one f(x)-value.
2. Examine the Table:
Let's look at the table of values provided:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
64.1 & 10 \\
-55.4 & 34.5 \\
-44 & -75.7 \\
64.1 & -73 \\
-55.9 & -97.7 \\
\hline
\end{array}
\][/tex]
3. Identify Duplicate x-Values:
- Notice that the x-value 64.1 appears twice in the table.
- The first time it appears, it maps to an f(x)-value of 10.
- The second time it appears, it maps to an f(x)-value of -73.
4. Check for Multiple Outputs:
- Since the x-value 64.1 is associated with two different f(x)-values (10 and -73), this violates the definition of a function.
5. Conclusion:
- Because there is at least one x-value (64.1) that does not map uniquely to a single f(x)-value, the relationship represented by the table does NOT qualify as a function.
Therefore, the answer is: No, the table does NOT represent a function.