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

a reflection over the y-axis

a rotation of 90° about the origin

a reflection over the x-axis

a reflection over y = x

Answer 1

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]}

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Answer 2

Theodore Abad

The transformation that transforms (p, q) to (q, p) is called a transposition or interchange transformation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

a reflection over the y-axis a rotation of 90° about the origin a reflection over the x-axis a reflection over y = x

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

a reflection over the y-axis

a rotation of 90° about the origin

a reflection over the x-axis

a reflection over y = x