Answer to Question #296493 in Calculus for ...

Question

Which graph represents the parametric equations x = 3t and y = t³ – 1, where –2 ≤ t ≤ 3?

Answer 1

$x=3t, y=t^3-1, t\in[-2,3]\\ x\in[-6,9],y\in[-9,26]\\ t=\frac{x}{3}\\ y=(\frac{x}{3})^3-1=\frac{x^3}{27}-1$

$y=\frac{x^3}{27}-1\\ \begin{matrix} x &-6&-3&0&3&6&9 \\ y & -9&-2&-1&0&9&26 \end{matrix}$