What are the domain and range of the function given here {(14,−6),(−12,6),(9,−1),(4,−6)}



Given the function defined by the set of points \(\{(14, -6), (-12, 6), (9, -1), (4, -6)\}\), we can determine the domain and range as follows:

### Domain:
- The domain of a function consists of all the **input values** (the first components in the ordered pairs).
- From the set of points:
  - The inputs (or \(x\)-values) are \(14\), \(-12\), \(9\), and \(4\).

Thus, the domain is \(\{14, -12, 9, 4\}\).

### Range:
- The range of a function consists of all the **output values** (the second components in the ordered pairs).
- From the set of points:
  - The outputs (or \(y\)-values) are \(-6\), \(6\), \(-1\), and \(-6\).

Thus, the range is \(\{-6, 6, -1\}\).

(Note that \(-6\) is repeated, but it only needs to be listed once in the range.)

If you have any more questions or would like more details, feel free to ask!

Here are 5 related questions to explore:

1. How do you find the domain and range for a continuous function like \(f(x) = x^2\)?
2. What would be the domain and range of the function \(g(x) = \sqrt{x-2}\)?
3. Can a function have the same range but different domains? Give an example.
4. What is the range of a linear function \(h(x) = 2x + 3\)?
5. How would the domain and range change if the function includes all real numbers within specific intervals?

**Tip:** The domain is the set of all possible input values for which the function is defined, while the range is the set of all possible outputs the function can produce.

Explore how to determine the domain and range of a function defined by a set of points such as {(14, -6), (-12, 6), (9, -1), (4, -6)}. This detailed explanation covers the inputs and outputs of the function, essential for high school students studying functions and mathematical analysis.

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