DeepCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.1 The Position Vector, #45 · Multivariable Calculus · Curves in space

Practice with parameters, starting from

Practice with parameters, starting from $x = F (t), y = G (t)$ .
(a) The mirror image across the $4 5^{\circ}$ line is $x =$ ____, $y =$ ____.
(b) Write the curve $x = t^{3}, y = t^{2}$ as $y = f (x)$ .
(c) Why can't $x = t^{2}, y = t^{3}$ be written as $y = f (x)$ ?
(d) If $F$ is invertible then $t = F^{- 1} (x)$ and $y =$ ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.1 The Position Vector, #45

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