Question

the graph of a one-to-one function f is given. draw the graph of the inverse function \\(f^{-1}\\). for convenience (and as a hint), the graph of \\(y = x\\) is also given.

Explanation:

Identify key points on the graph of \(f\)

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Reflect points across the line \(y = x\) to find points on \(f^{-1}\)

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Connect the reflected points sequentially

$$ \text{Segments: } (-5, -5) ightarrow (0, -4) ightarrow (2, 1) ightarrow (3, 2) $$

Answer:

To graph the inverse function \(f^{-1}\), reflect the key points of the given function \(f\) across the line \(y = x\) by swapping their \(x\)- and \(y\)-coordinates:

• The point \((-5, -5)\) reflects to \((-5, -5)\).
• The point \((-4, 0)\) reflects to \((0, -4)\).
• The point \((1, 2)\) reflects to \((2, 1)\).
• The point \((2, 3)\) reflects to \((3, 2)\).

Plot these reflected points and connect them with straight line segments in order: from \((-5, -5)\) to \((0, -4)\), then to \((2, 1)\), and finally to \((3, 2)\).