The image contains three mathematical questions related to functions. Let's address each one:

1. Question 1:

   • Function: $f : \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$
   • Question: What is the domain of this function?
   • Answer: The domain of this function is all real numbers $\mathbb{R}$ because the function $x^2$ is defined for any real number $x$. The correct choice is $\mathbb{R}$.

2. Question 2:

   • Function: $f : \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$
   • Question: What is the codomain of this function?
   • Answer: The codomain is the set the function maps to, which is given as $\mathbb{R}$. The correct choice is $\mathbb{R}$.

3. Question 3:

   • Function: $f : \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$
   • Question: What is the range of this function?
   • Answer: The range of $f(x) = x^2$ includes all non-negative real numbers, since squaring any real number results in a value $\geq 0$. Therefore, the range is $\mathbb{R}_{\geq 0}$, often denoted as $[0, \infty)$. The correct choice is $\mathbb{R}_{\geq 0}$ or equivalent notation.

Would you like further details on these solutions?

Here are 5 related questions to expand understanding:

1. What is the difference between codomain and range of a function?
2. How would the domain change if the function were $f(x) = \frac{1}{x}$?
3. If the function were $f(x) = x^3$, what would be the range?
4. Can a function’s range ever exceed its codomain?
5. How does the graph of $f(x) = x^2$ help visualize the domain and range?

Tip: The domain represents the set of all possible input values, while the range represents the actual output values that the function can produce from the given domain.