Applying the rules that makes a relation a function:
1. The relation that doesn't represent y as a function of x is: D. Answer J.
2. The only set of ordered pairs showing a relation that represents y as a function of x is: A) {(-9, 2), (0, 6), (1, -2), (-3, 6)}.
Recall:
- A relation is a function if every input value (x-value) has only one possible y-value that is related to or corresponds to.
Let's analyze each relation given:
1. All the relations in F, H, and G all have only one y-value assigned or related to every x-value (input). Hence, they all represent y as a function of x.
The graph in J does not represent y as a function of x because of the following:
- x =-3 has two y-values, -2, and -3
- x = -2 has two y-values, 0, and -1.
- x = -1 has two y-values, 1, and 2.
- x = 0 has two y-values, 3, and 4.
Therefore, answer J does not represent a function.
2. Same rule of a function applies here.
- From the set of ordered pairs given, only the set of ordered pairs in A represents y as a function of x because it every of its x-values has only one possible y-value assigned to them.
- The rest set of ordered pairs have more than one y-values assigned to some of their x-values.
In summary:
1. The relation that doesn't represent y as a function of x is: D. Answer J.
2. The only set of ordered pairs showing a relation that represents y as a function of x is: A) {(-9, 2), (0, 6), (1, -2), (-3, 6)}.
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