Question

Use this mapping diagram of f(x) to answer the questions

2- — 4
-1 — 1
0 — 0
1 — 1
2 — 4

What is the domain of *f*(x)? {0, 1, 4} or {-2, -1, 0, 1, 2}
What is the range of f(x)? {-2, 1- 0, 1, 2} or {0, 1, 4}

Answer 1

To determine the domain and range of the function \( f(x) \) based on the provided mapping diagram, let's analyze the pairs in the mapping:

**Mapping provided:**
- \( f(-2) = 4 \)
- \( f(-1) = 1 \)
- \( f(0) = 0 \)
- \( f(1) = 1 \)
- \( f(2) = 4 \)

### Domain of \( f(x) \)
The domain consists of all the input values (x-values) that are mapped. The x-values from the mapping are:
- -2
- -1
- 0
- 1
- 2

Thus, the domain of \( f(x) \) is:
\[
\text{Domain: } \{-2, -1, 0, 1, 2\}
\]

### Range of \( f(x) \)
The range consists of all the output values (y-values) that the function produces for the given input values. The output values from the mapping are:
- 4 (from both -2 and 2)
- 1 (from both -1 and 1)
- 0 (from 0)

Therefore, the unique output values, thus the range is:
\[
\text{Range: } \{0, 1, 4\}
\]

### Conclusion
- The domain of \( f(x) \) is \( \{-2, -1, 0, 1, 2\} \).
- The range of \( f(x) \) is \( \{0, 1, 4\} \).