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50 points, Based on the table, write a function rule that represents the relationship between x and y.

50 points, Based on the table, write a function rule that represents the relationship-example-1

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Answer:

y = (1/2)|x -8| -3

Explanation:

The first five points fall on a straight line with a slope of ...

∆y/∆x = -0.5/1 = -0.5

The last point is not on that line.

So, several options are available:

  • write a piecewise function with f(10) having a special definition: y={1-x/2, x≠10; -2, x=10}
  • write a piecewise function with any definition for x > 5 such that f(10) = -2: y={1-x/2, x≤6; -2, x>6}
  • use a function, such as absolute value, that changes slope in a way that makes f(10) = -2. Such a function is shown in the first attached graph
  • simply list the points. Such a list is a "function rule". (x, y) ∈ {(1, 0.5), (2, 0), (3, -0.5), (4, -1), (5, -1.5), (10, -2)}.
50 points, Based on the table, write a function rule that represents the relationship-example-1
50 points, Based on the table, write a function rule that represents the relationship-example-2
50 points, Based on the table, write a function rule that represents the relationship-example-3
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