逐个分析并绘制该题目四个选项的函数图像---**Question Stem:** 6. 函数 f(x) = x² / (2ˣ - 2⁻ˣ) 的部分图像大致为 **Mathematical Formula:** f(x) = x² / (2ˣ - 2⁻ˣ) **Options:** **A.** * **Chart Type:** Graph of a function. * **Main Elements:** * **Coordinate Axes:** A horizontal X-axis labeled 'x' with an arrow pointing right, and a vertical Y-axis labeled 'y' with an arrow pointing up. * **Origin:** Labeled 'O' at the intersection of the axes. There is an open circle (hole) at the origin. * **Curve:** The graph consists of two branches. Both branches are located entirely above the X-axis. The curve is symmetric with respect to the Y-axis. As x approaches the origin from either the left or the right, the curve approaches the open circle at the origin. The curve descends towards the origin from the left and right, then extends upwards away from the origin as |x| increases. **B.** * **Chart Type:** Graph of a function. * **Main Elements:** * **Coordinate Axes:** A horizontal X-axis labeled 'x' with an arrow pointing right, and a vertical Y-axis labeled 'y' with an arrow pointing up. * **Origin:** Labeled 'O' at the intersection of the axes. There is an open circle (hole) at the origin. * **Curve:** The graph consists of two branches, forming a curve that passes through the first and third quadrants (with a hole at the origin). For x > 0, the curve is above the X-axis and appears to be increasing. For x < 0, the curve is below the X-axis and appears to be increasing (becoming less negative, or decreasing in absolute value) as x approaches the origin, and decreasing (becoming more negative) as x moves further left. The curve exhibits rotational symmetry about the origin. As x approaches the origin from either the left or the right, the curve approaches the open circle at the origin. **C.** * **Chart Type:** Graph of a function. * **Main Elements:** * **Coordinate Axes:** A horizontal X-axis labeled 'x' with an arrow pointing right, and a vertical Y-axis labeled 'y' with an arrow pointing up. * **Origin:** Labeled 'O' at the intersection of the axes. There is an open circle (hole) at the origin. * **Curve:** The graph consists of two branches. Both branches are located entirely below the X-axis. The curve is symmetric with respect to the Y-axis. As x approaches the origin from either the left or the right, the curve approaches the open circle at the origin. The curve ascends towards the origin from the left and right, then extends downwards away from the origin as |x| increases. **D.** * **Chart Type:** Graph of a function. * **Main Elements:** * **Coordinate Axes:** A horizontal X-axis labeled 'x' with an arrow pointing right, and a vertical Y-axis labeled 'y' with an arrow pointing up. * **Origin:** Labeled 'O' at the intersection of the axes. There is an open circle (hole) at the origin. * **Curve:** The graph consists of two branches, forming a curve that passes through the second and fourth quadrants (with a hole at the origin). For x > 0, the curve is below the X-axis and appears to be decreasing. For x < 0, the curve is above the X-axis and appears to be decreasing (becoming less positive, or increasing in absolute value) as x approaches the origin, and increasing (becoming more positive) as x moves further left. The curve exhibits rotational symmetry about the origin. As x approaches the origin from either the left or the right, the curve approaches the open circle at the origin.