The graph below consists of three points connected by line segments. You can dra

Question

The graph below consists of three points connected by line segments. You can drag Point1 and Point3 to new positions; as you do, the line segments connected to the points will be updated. Point2 cannot be dragged. Drag Point1 and Point3 so that the resulting graph has he following three properties: The graph is the graph of a function f. The function f has an inverse. f(6) notequalto 6, however f has the property that f(6) = f^-1(6). When you are satisfied with your graph, click the Save Answer button. You answered this question 1 time. You can attempt this question 4 times. Your answer was interpreted as: You placed Point1 and Point3 at (-8, 3) and (2, -7). Your answer is not correct. According to your graph, f(6) is undefined since there is no point with an x coordinate of 6 on the graph of f that is shaded in.

Explanation / Answer

From the graph, we observe that that the 3 given points are (-8,3) , (-6, 1) and (2,-7). Apparently, the graph given is that of a straight line which passes through the above 3 points. The slope of a line passing through the points (-8,3) and

(-6, 1) is (1-3)/ [-6-(-8)] = -2/2 = -1. Also the y -intercept (where x = 0) is -5.Thus, the equation of the line is y = f(x ) = - x - 5. ( the slope -intercept form of the equation of a line is y = mx + c where m is the slope and c is the y-intercept).

1. The equation of the function is y = f ( x ) = -x - 5.

2. Since y = -x - 5, therefore x = -y -5. On interchanging x and y, the inverse function is f-1 (x ) = y = -x- 5. Thus f is its own inverse.

3. On substituting x = 6 in the equation of f (x), we get f (6) = -6 -5 = -11 6. Also f (6) = f-1(6) = 11

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