Final answer:
None of the options provided can be correct for the point through which the tangent line at (9, -6) passes, given the slope from Figure A1 is 3. The slope calculation shows that none of the points listed have a slope of 3 when connected to (9, -6).
Step-by-step explanation:
The question asks to determine which point the tangent line to the curve y = f(x) at the point (9, -6) passes through. Since we do not know the function f(x) directly, we will assume that the slope of this tangent line is the same as the slope given in Figure A1. Figure A1 states that the slope of the line graphed there is 3, meaning the vertical change (rise) is 3 units for every 1 unit of horizontal change (run).
To find a point that this tangent line passes through, we can use the slope to calculate where this line would intersect other points on the graph. Starting from the point (9, -6), if we move horizontally by 1 unit, we will rise by 3 units vertically because the slope is 3. However, none of the options provided involves moving in the positive x-direction; they all concern points that are at an equal distance from the y-axis but on the opposite side. For point 1) (-9, 6), the horizontal change from 9 to -9 is -18 units, so the vertical change would need to be -18*3 which gives -54 to maintain the slope of 3. Adding -54 to the y-coordinate of -6, we would end up at a y-coordinate of -60, not 6. This process of elimination will reveal that none of the provided options fit the criteria of having a slope of 3 when connected to the point (9, -6). Without further context or additional information, we conclude that the tangent line at (9, -6) does not pass through any of the points listed in the options.