Question

r is graphed below in black squares.

a) what is the inverse of \\(r\\)? graph the inverse in the window below by dragging the blue points.

b) is the inverse of \\(r\\) a function?

yes
no
not enough information given

Explanation:

Identify points of relation \(R\)

$$ R = \{(-7, -2), (-5, 6), (-3, 4), (-2, 2), (1, 6), (3, 7), (6, 3), (8, -5)\} $$

Find inverse relation \(R^{-1}\)

$$ R^{-1} = \{(-2, -7), (6, -5), (4, -3), (2, -2), (6, 1), (7, 3), (3, 6), (-5, 8)\} $$

Determine if the inverse is a function

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Answer:

Question a

The inverse of \(R\) is the set of points obtained by swapping the \(x\)- and \(y\)-coordinates of each point in \(R\):

$$ R^{-1} = \{(-2, -7), (6, -5), (4, -3), (2, -2), (6, 1), (7, 3), (3, 6), (-5, 8)\} $$

Question b

• Yes
• No (Correct answer)
• Not enough information given