(b) Find the domain D and range R of the function f when given the following points (0,2) and (6,-2). (Enter your answers using interval notation.)


Given two points \((0, 2)\) and \((6, -2)\), let's find the **domain (D)** and **range (R)** of the function \(f\). We can treat these points as lying on a line between \(x = 0\) and \(x = 6\).

### Domain (D):
The domain consists of all the possible \(x\)-values of the function. Since the function is only defined at and between the \(x\)-values of the given points, the domain is:
\[
D = [0, 6]
\]
This means that the function is defined from \(x = 0\) to \(x = 6\), inclusive.

### Range (R):
The range consists of all the possible \(y\)-values the function can take. The function passes through \(y = 2\) at \(x = 0\) and \(y = -2\) at \(x = 6\). Since we assume the function is linear (unless otherwise stated), the \(y\)-values range between 2 and -2. Therefore, the range is:
\[
R = [-2, 2]
\]
This indicates that the function takes all values from \(-2\) to \(2\), inclusive.

### Final Answer:
- **Domain**: \( D = [0, 6] \)
- **Range**: \( R = [-2, 2] \)

Would you like further details or explanations on this? 

Here are 5 related questions to explore:
1. How would the domain and range change if the function was quadratic instead of linear?
2. What is the equation of the line passing through these two points?
3. Can a function's domain ever be larger than the input points provided?
4. How would you find the slope between these two points?
5. What if the function was not continuous—how would that affect the domain and range?

**Tip:** Always remember that the domain of a function includes all \(x\)-values for which the function is defined, and the range includes all resulting \(y\)-values from that domain.

Find the domain D and range R of the function f when given the following points (0,2) and (6,-2). (Enter your answers using interval notation.)

Discover how to find the domain and range of a linear function given two points (0, 2) and (6, -2). This problem involves the concepts of linear functions, interval notation, and coordinate geometry, suitable for students in Grades 9-11.

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