The discussion focuses on graphing the vector function r(t) = t²i + t³j for the range -∞ < t < ∞. Participants confirm that it is valid to substitute a specific t value into t² for the x-coordinate and the same t value into t³ for the y-coordinate. For instance, when t = 0, the resulting point on the graph is (0, 0). This method allows for the accurate plotting of the curve defined by the vector function.
PREREQUISITESStudents studying calculus, particularly those learning about vector functions and parametric equations, as well as educators looking for teaching strategies in graphing techniques.
Sure. Each point on the graph of this function corresponds to a particular value of t, so when t = 0, for example, you get the point (0, 0).stau40 said:Homework Statement
Sketch the curve given by the vector valued function r(t)=t^2i + t^3j, -infinity<t<infinity
Homework Equations
The Attempt at a Solution
I'm confused with how to graph it when it's not two separate values separated with a comma. Am I allowed to plug in a t value for t^2 to get the x coordinate then plug in the same t value for t^3 to get the y coordinate?