Question

Which of the following sets of parametric equations represent the curve y=x³, where x∈ℝ? to receive credit, you must select all correct choices.

a. x=t^9, y=t³, t∈ℝ
b. x=t+1, y=(t+1)³, t∈ℝ
c. x=(t+1)³, y=t+1, t∈ℝ
d. x=–t³, y=–t, t∈ℝ
e. x=sin(t), y=cos(t), 0≤t≤2π
f. x=–t, y=–t³, 0≤t≤2π
g. x=–t, y=–t³, t∈ℝ
h. x=t³, y=t, t∈ℝ
i. x=t³, y=t^9, t∈ℝ
j. x=t, y=t³, 0≤t≤2π
k. x=t, y=t³, t∈ℝ
l. x=sin(t), y=cos(t), t∈ℝ

Answer 1

• b. x=t+1, y=(t+1)³, t∈ℝ
• g. x=–t, y=–t³, t∈ℝ
• i. x=t³, y=t^9, t∈ℝ
• k. x=t, y=t³, t∈ℝ

Explanation:

You want the parametric equations equivalent to y = x³.

Equivalent relation

The relation will be equivalent if cubing the expression for x gives the expression for y. The possible values of x must include all real numbers.

These conditions are met for ...

• b. x=t+1, y=(t+1)³, t∈ℝ
• g. x=–t, y=–t³, t∈ℝ
• i. x=t³, y=t⁹, t∈ℝ
• k. x=t, y=t³, t∈ℝ

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