Mathematics

The key is to check where each piece of the function is increasing, then verify continuity at the boundary. For the parabola $x^2 + 2x$ on $(-\infty, 1]$, find where its derivative is positive—this tells you which part of that piece slopes upward. For the linear piece $3x - 1$ on $(1, \infty)$, the slope is constant. Finally, make sure your answer accounts for the actual domain where each piece applies.

The key is to check where each piece of the function is increasing, then verify continuity at the boundary. For the parabola $x^2 + 2x$ on $(-\infty, 1]$, find where its derivative is positive—this tells you which part of that piece slopes upward. For the linear piece $3x - 1$ on $(1, \infty)$, the slope is constant. Finally, make sure your answer accounts for the actual domain where each piece applies.