nsider the function \( f(x)=-(x-2)^{3}+8 \). What is the domain of this function? (1 point) \( (2, \infty) \) \( (-\infty, 2) \) \( (-\infty, \infty) \) \( (-\infty, 2) \)

The function \( f(x)=-(x-2)^{3}+8 \) is a polynomial function, and polynomial functions have a domain of all real numbers. This means that you can plug in any real value for \( x \) without running into issues like division by zero or taking the square root of a negative number. So, the correct answer is \( (-\infty, \infty) \). Additionally, polynomial functions are known for their smooth curves and continuous nature, indicating there are no gaps or breaks in their graphs. For \( f(x) \), as \( x \) approaches positive or negative infinity, the function will also approach infinity, exhibiting the usual behavior of cubic functions influenced by translation and reflection.