1. The problem asks to identify which graph (a, b, c, or d) could represent the original function $y = f(x)$ given that the opposite figure represents its first derivative $f'(x)$. 2. The given function $f(x)$ is a parabola opening upwards, which is a quadratic function. Its first derivative $f'(x)$ should be a linear function because the derivative of a quadratic is linear. 3. Among the options: - Graph a shows a wavy curve crossing the x-axis twice, which is not linear. - Graph b shows a curve crossing the x-axis twice, also not linear. - Graph c shows a curve crossing the x-axis three times, not linear. - Graph d shows a straight line passing through the origin, which is linear. 4. Since the first derivative of a parabola is a linear function, the opposite figure (the first derivative) must be a straight line. 5. Therefore, the original function $f(x)$ corresponds to the parabola, and the first derivative corresponds to graph d. Final answer: The general shape of the function $y = f(x)$ is a parabola, and the first derivative is represented by graph d (a straight line).