Decide whether the relation defines \( y \) as a function of \( x \). Give the domain and range. \( y=x^{9} \)

Absolutely, the relation \( y = x^{9} \) defines \( y \) as a function of \( x \). This is because for every input \( x \), there is exactly one output \( y \). In simpler terms, if you pick a number, raise it to the ninth power, and you’ll always get a unique result! Now, let’s talk about the domain and range. The domain of this function is all real numbers \((-∞, ∞)\) since you can input any real number for \( x \). As for the range, since \( x^{9} \) is an odd power, \( y \) can take on all real values as well, which means the range is also \((-∞, ∞)\). Happy graphing!