Short Answer

In Exercises 19–21 sketch the graph of a vector-valued function $r (t) = (x (t), y (t))$ with the specified properties. Be sure to indicate the direction of increasing values of t.
Domain
$t \in ℝ, r (2) = (1, 1), r (0) = (- 3, 3), r (- 2) = (- 5, - 5) \lim_{t \to - \infty} x (t) = \infty, \lim_{t \to - \infty} y (t) = - \infty, and \lim_{t \to \infty} r (t) = (0, 0) .$

The graph of the given vector-valued function with the specified properties is

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Step 1. Given Information.

The given vector-valued function is $r (t) = (x (t), y (t)) .$ The given specified properties are $t \in ℝ, r (2) = (1, 1), r (0) = (- 3, 3), r (- 2) = (- 5, - 5) \lim_{t \to - \infty} x (t) = \infty,$

$\lim_{t \to - \infty} y (t) = - \infty, and \lim_{t \to \infty} r (t) = (0, 0) .$

Step 2. Sketch the graph.

The graph of the given vector-valued function with the specified properties is

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Step 1. Given Information.

Step 2. Sketch the graph.

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Short Answer

In Exercises 19–21 sketch the graph of a vector-valued function r(t)=x(t), y(t) with the specified properties. Be sure to indicate the direction of increasing values of t.Domain t∈ℝ, r2=1,1, r0=-3,3, r-2=-5,-5 limt→-∞x(t)=∞,limt→-∞y(t)=-∞, and limt→∞r(t)=0,0.

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Step 1. Given Information.

Step 2. Sketch the graph.

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