### Instruction: Given that $f(x) = x^k$ where $k > 0$, what is the range of $f(x)$ on the interval $[1, \infty)$?### Response: So we know that $f(x) = x^k$ where $k > 0$.
And we want to find the range of $f(x)$ on the interval $[1, \infty)$.
Right. So we know that $f(x)$ is a continuous function.
And we know that $f(1) = 1^k = 1$.
And we also know that as $x$ approaches infinity, $f(x)$ approaches infinity.