Determine whether the relation defines a function, and give the domain and range.

Ask by Campos Ball. in the United States

Dec 04,2024

Question

Determine whether the relation defines a function, and give the domain and range. $$ \{(-7,4),(8,4),(-9,5)\} $$

UpStudy AI · Accepted Answer

To determine whether the relation defines a function, we need to check if each input (or first element of each ordered pair) is associated with exactly one output (or second element of each ordered pair).

The given relation is:
$$
\{(-7,4),(8,4),(-9,5)\}
$$

Let's analyze the ordered pairs:

1. The first pair is $$(-7, 4)$$. The input is $$-7$$ and the output is $$4$$.
2. The second pair is $$(8, 4)$$. The input is $$8$$ and the output is $$4$$.
3. The third pair is $$(-9, 5)$$. The input is $$-9$$ and the output is $$5$$.

Now, we check the inputs:
- The input $$-7$$ corresponds to the output $$4$$.
- The input $$8$$ corresponds to the output $$4$$.
- The input $$-9$$ corresponds to the output $$5$$.

Since each input $$-7$$, $$8$$, and $$-9$$ is associated with exactly one output, the relation does define a function.

Next, we can determine the domain and range:

- **Domain**: The set of all first elements (inputs) in the ordered pairs. Thus, the domain is:
  $$
  \{-7, 8, -9\}
  $$

- **Range**: The set of all second elements (outputs) in the ordered pairs. Thus, the range is:
  $$
  \{4, 5\}
  $$

In summary:
- The relation defines a function.
- Domain: $$\{-7, 8, -9\}$$
- Range: $$\{4, 5\}$$
The relation defines a function. Domain: $$\{-7, 8, -9\}$$, Range: $$\{4, 5\}$$

Determine whether the relation defines a function, and give the domain and range.

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