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Sagot :
Sure, let's analyze each set of pairs to determine whether they represent a function. As a reminder, a relation is considered a function if each [tex]\( x \)[/tex]-value in the relation is paired with exactly one [tex]\( y \)[/tex]-value.
1. First Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & 10 \\ \hline -3 & 5 \\ \hline -3 & 4 \\ \hline 0 & 0 \\ \hline 5 & -10 \\ \hline \end{array} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-5, -3, -3, 0, 5\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(-3\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(5\)[/tex] and [tex]\(4\)[/tex].
- Since [tex]\(-3\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, the first table does not represent a function.
2. Second Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & -3 \\ \hline -1 & -2 \\ \hline 0 & -1 \\ \hline 0 & 0 \\ \hline 1 & -1 \\ \hline \end{array} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-2, -1, 0, 0, 1\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(0\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(-1\)[/tex] and [tex]\(0\)[/tex].
- Since [tex]\(0\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, the second table does not represent a function.
3. Set of Pairs:
[tex]\[ \{(-12, 4), (-6, 10), (-4, 15), (-8, 18), (-12, 24)\} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-12, -6, -4, -8, -12\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(-12\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(4\)[/tex] and [tex]\(24\)[/tex].
- Since [tex]\(-12\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, this set does not represent a function.
Therefore, none of the given tables or sets represent a function since each has at least one [tex]\( x \)[/tex]-value associated with more than one [tex]\( y \)[/tex]-value.
1. First Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & 10 \\ \hline -3 & 5 \\ \hline -3 & 4 \\ \hline 0 & 0 \\ \hline 5 & -10 \\ \hline \end{array} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-5, -3, -3, 0, 5\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(-3\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(5\)[/tex] and [tex]\(4\)[/tex].
- Since [tex]\(-3\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, the first table does not represent a function.
2. Second Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & -3 \\ \hline -1 & -2 \\ \hline 0 & -1 \\ \hline 0 & 0 \\ \hline 1 & -1 \\ \hline \end{array} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-2, -1, 0, 0, 1\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(0\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(-1\)[/tex] and [tex]\(0\)[/tex].
- Since [tex]\(0\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, the second table does not represent a function.
3. Set of Pairs:
[tex]\[ \{(-12, 4), (-6, 10), (-4, 15), (-8, 18), (-12, 24)\} \][/tex]
- Here, we have the [tex]\( x \)[/tex]-values: [tex]\(-12, -6, -4, -8, -12\)[/tex].
- Notice that the [tex]\( x \)[/tex]-value [tex]\(-12\)[/tex] is repeated, but paired with different [tex]\( y \)[/tex]-values [tex]\(4\)[/tex] and [tex]\(24\)[/tex].
- Since [tex]\(-12\)[/tex] is associated with two different [tex]\( y \)[/tex]-values, this set does not represent a function.
Therefore, none of the given tables or sets represent a function since each has at least one [tex]\( x \)[/tex]-value associated with more than one [tex]\( y \)[/tex]-value.
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