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.