Question
When graphing the function mc026-1.jpg on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?
Xmin: –10, Xmax: 10
Ymin: –10, Ymax: 10
Xmin: –5, Xmax: 5
Ymin: –5, Ymax: 5
Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10
Xmin: –10, Xmax: 0
Ymin: –10, Ymax: 0
Xmin: –10, Xmax: 10
Ymin: –10, Ymax: 10
Xmin: –5, Xmax: 5
Ymin: –5, Ymax: 5
Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10
Xmin: –10, Xmax: 0
Ymin: –10, Ymax: 0
Answers
Answered by
GPT-4o mini
To choose the most appropriate viewing window for graphing a function and determining its domain and range, it's important to consider the characteristics of the function itself, particularly the type of function.
While I don't have access to the specific image mc026-1.jpg to assess the function directly, I can guide you on how to make an appropriate choice based on typical types of functions:
1. **Check the nature of the function:** If it’s a polynomial, rational, exponential, or trigonometric function, the choice of window could vary.
2. **Choosing the range:**
- If the function has limits (like an exponential approaching zero), then a window that captures where the function values stabilize could be useful.
- If it spans negative and positive values significantly, wider options might be helpful.
3. **Finding the domain:**
- If the function has vertical asymptotes or is defined only over a certain interval, you want to ensure that your x-values cover that interval.
### Given The Options:
- **Xmin: –10, Xmax: 10; Ymin: –10, Ymax: 10** - This is a wide range that can help identify general trends in the function.
- **Xmin: –5, Xmax: 5; Ymin: –5, Ymax: 5** - This is a narrower range, which may be useful if the function has important behavior in this interval.
- **Xmin: 0, Xmax: 10; Ymin: 0, Ymax: 10** - This is for functions that are only increasing in the positive quadrant or where the function is at least non-negative.
- **Xmin: –10, Xmax: 0; Ymin: –10, Ymax: 0** - For functions that are strictly negative or defined within negative bounds.
**Recommendation:** If you are unsure of the function, the most general choice is **Xmin: –10, Xmax: 10; Ymin: –10, Ymax: 10**. This wider window allows you to capture the entire behavior of most functions, including their domain and range more effectively.
While I don't have access to the specific image mc026-1.jpg to assess the function directly, I can guide you on how to make an appropriate choice based on typical types of functions:
1. **Check the nature of the function:** If it’s a polynomial, rational, exponential, or trigonometric function, the choice of window could vary.
2. **Choosing the range:**
- If the function has limits (like an exponential approaching zero), then a window that captures where the function values stabilize could be useful.
- If it spans negative and positive values significantly, wider options might be helpful.
3. **Finding the domain:**
- If the function has vertical asymptotes or is defined only over a certain interval, you want to ensure that your x-values cover that interval.
### Given The Options:
- **Xmin: –10, Xmax: 10; Ymin: –10, Ymax: 10** - This is a wide range that can help identify general trends in the function.
- **Xmin: –5, Xmax: 5; Ymin: –5, Ymax: 5** - This is a narrower range, which may be useful if the function has important behavior in this interval.
- **Xmin: 0, Xmax: 10; Ymin: 0, Ymax: 10** - This is for functions that are only increasing in the positive quadrant or where the function is at least non-negative.
- **Xmin: –10, Xmax: 0; Ymin: –10, Ymax: 0** - For functions that are strictly negative or defined within negative bounds.
**Recommendation:** If you are unsure of the function, the most general choice is **Xmin: –10, Xmax: 10; Ymin: –10, Ymax: 10**. This wider window allows you to capture the entire behavior of most functions, including their domain and range more effectively.