What transformation transforms (p, q) to (q, p)?

Question

a reflection over the y-axis

a rotation of 90° about the origin

a reflection over the x-axis

a reflection over y = x

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Answer 1 · 2016-10-26T09:38:05

If we wish to map $p->q$ and $q->p$ , we are inverting the function. An inversion can be accomplished by reflecting over $y = x$ .

For example, take $y = x^2$ . Now switch $y$ and $x$ , and solve for $y$ .

$x = y^2$

$y = pmsqrt(x)$

Both ( $pm$ ) of these functions then combine to form the inverse.

Original
graph{x^2 [-10, 10, -5, 5]}

Inverse ( $(p,q) -> (q,p)$ )
graph{(y - sqrt(x))(y + sqrt(x)) = 0 [-10, 10, -5, 5]}