https://file.aiquickdraw.com/mathbot/file/1726354398514q3nhmq8y.jpg

The image shows a graph with three functions \( f \), \( g \), and \( h \). The question asks: **"Which of these functions have a domain of all real numbers?"**

### Analysis:
1. **Function \( f \) (blue curve)**: This appears to be a quadratic function (parabola) that opens upwards. Quadratic functions generally have a domain of all real numbers.
2. **Function \( g \) (green line)**: This is a straight line, meaning it is a linear function. Linear functions also have a domain of all real numbers.
3. **Function \( h \) (red curve)**: This function resembles a portion of a parabola. However, the curve is only drawn starting at some point and extends to the right, suggesting a restriction on the domain (possibly a square root function or something similar). Therefore, this function likely does **not** have a domain of all real numbers.

### Conclusion:
- Functions \( f \) (blue) and \( g \) (green) have a domain of all real numbers.
- Function \( h \) (red) does not.

Would you like more details on the domain of these functions or have any other questions?

### Related Questions:
1. What are the general domain and range of quadratic functions?
2. How do you determine the domain of a square root function?
3. Can a function have a domain restriction even if it looks continuous over part of the graph?
4. How does the domain of a rational function differ from other types of functions?
5. What is the significance of a function's domain in solving real-world problems?

### Tip:
For any function, the domain consists of all the input values (x-values) where the function is defined, meaning it produces a real number result.

Which of these functions have a domain of all real numbers?

This problem explores the domain of various functions, including quadratic, linear, and potentially restricted functions. We determine which functions have a domain of all real numbers and discuss domain limitations for certain types of functions.

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