Determine if the function \( y=x^{2}-x \) is one-to-one. Select an answer \( v \)

To determine if the function \( y = x^2 - x \) is one-to-one, we can analyze its behavior. A function is one-to-one if every horizontal line intersects the graph at most once. The function \( y = x^2 - x \) is a parabola that opens upwards, indicating it will have a minimum point and thus can intersect horizontal lines more than once. By calculating the derivative \( y' = 2x - 1 \), we find that it equals zero at \( x = \frac{1}{2} \), confirming the presence of a vertex. This means the function is decreasing until \( x = \frac{1}{2} \) and increasing afterward, which indicates that \( y = x^2 - x \) is not one-to-one. In conclusion, the function \( y = x^2 - x \) is not a one-to-one function. To confirm this, you could select specific values of \( x \) like \( x = 0 \) and \( x = 1 \), both giving a result of \( y = 0 \), showcasing that two different inputs yield the same output.