https://file.aiquickdraw.com/mathbot/file/17299163264645hypgz4d.jpg

To solve this problem, let’s examine the graph closely and provide the requested domain and range.

1. **Restricted Domain**:
   - The graph is a sinusoidal function that oscillates symmetrically around the y-axis.
   - To include \( x = 0 \), let’s select a domain that covers one complete cycle. Observing the graph, one full cycle appears to extend from \( x = -\pi \) to \( x = \pi \).
   - Therefore, a restricted domain that includes \( x = 0 \) is:
     \[
     -\pi \leq x \leq \pi
     \]

2. **Range**:
   - The function oscillates vertically between a maximum value of \( y = 2 \) and a minimum value of \( y = -2 \).
   - Thus, the range of the function is:
     \[
     -2 \leq y \leq 2
     \]

### Final Answer:
- **Restricted Domain**: \( -\pi \leq x \leq \pi \)
- **Range**: \( -2 \leq y \leq 2 \)

Would you like a more detailed explanation or have any other questions?

---

Here are some related questions to deepen your understanding:

1. What is the period of the sinusoidal function shown in the graph?
2. How would the range change if the amplitude of the function were increased?
3. What would the domain be if we wanted to include two complete cycles around \( x = 0 \)?
4. How does changing the frequency of a sinusoidal function affect its domain for one cycle?
5. If we shift the graph vertically by 1 unit up, what will be the new range?

**Tip:** Remember that the range of a sinusoidal function is determined by its amplitude and any vertical shifts.

For the graph below, give a restricted domain that includes x = 0 and the entire range of the function.

Learn how to find a restricted domain that includes x = 0 and determine the range of a sinusoidal function from its graph. This problem covers concepts of trigonometry, domain, and range for sinusoidal functions, suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation