Thank you for visiting Determine whether the relationship represented by the table is a function tex begin tabular c c hline x f x hline 64 1 10 55. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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.
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