The given function is defined as $f(x) = x$ for the domain $[-4, 2]$. Let’s address each question step by step:

1. Minimum Point

For the function $f(x) = x$, the output value is the same as the input value. Therefore:

• The minimum point occurs at the smallest value of $x$ in the domain, which is $x = -4$.
• Thus, $f(-4) = -4$. Minimum point: $(-4, -4)$.

2. Maximum Point

Similarly:

• The maximum point occurs at the largest value of $x$ in the domain, which is $x = 2$.
• Thus, $f(2) = 2$. Maximum point: $(2, 2)$.

3. Investigating Bijection (One-to-One and Onto)

The function $f(x) = x$ is:

• One-to-One: Each input $x$ produces a unique output $f(x)$. This property holds because the function is linear with a slope of 1.
• Onto: For every $y$ in the range $[-4, 2]$, there exists an $x$ in the domain $[-4, 2]$ such that $f(x) = y$. Thus, the function is onto.

Conclusion: $f(x) = x$ is a bijective function in the domain $[-4, 2]$.

Summary of Results:

1. Minimum point: $(-4, -4)$.
2. Maximum point: $(2, 2)$.
3. The function $f(x) = x$ is bijective in the given domain.

Do you want further clarifications or additional examples? Here are 5 related questions to expand on this:

1. How do you determine the range of a function for a given domain?
2. What are the conditions for a function to be bijective?
3. Can a quadratic function have a bijective property on any interval?
4. What would the minimum and maximum points be if the domain was extended to $[-5, 3]$?
5. How do you analyze one-to-one properties for non-linear functions?

Tip: For linear functions like $f(x) = x$, the minimum and maximum points directly correspond to the endpoints of the domain.