Use the definition of a one-to-one function to determine if the function is one-to-one.
\[
q(x)=x^{3}-17
\]
The function is one-to-one.
The function is not one-to-one.
Answer
\(\boxed{\text{The function is one-to-one.}}\)
Step 1 ：Use the definition of a one-to-one function to determine if the function is one-to-one.
Step 2 ：To determine if a function is one-to-one, we need to check if every output value corresponds to exactly one input value.
Step 3 ：For any two different input values, the output values must also be different.
Step 4 ：For the given function \(q(x)=x^{3}-17\), we can use the fact that the cube function \(x^{3}\) is a one-to-one function.
Step 5 ：Subtracting 17 from \(x^{3}\) does not change the one-to-one property of the function.
Step 6 ：\(\boxed{\text{The function is one-to-one.}}\)
