Question

In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ \u003c t \u003c ∞

Accepted Answer

Understand the parametric equations given: $$x = 2t$$ and $$y = |t - 1|$$, where $$t$$ ranges over all real numbers from $$-\infty to$$ $$\infty. $$The goal is to plot points $$(x, y) on $$the plane as $$t$$ changes and show the direction of increasing $$t. $$Recognize that $$y = |t - 1| is a $$piecewise function. For $$t \u003c 1$$, $$y = 1 - t$$, and for $$t \geq 1$$, $$y = t - 1. $$This will affect how the curve behaves on either side of $$t = 1. $$Create a table of values by choosing several values of $$t ($$for example, $$t = 0, 0.5, 1, 1.5, 2$$ and also some negative values like $$t = -1, -0.5). $$For each $$t$$, calculate $$x = 2t$$ and $$y = |t - 1| to $$get points $$(x, y) to $$plot. Plot the points on the coordinate plane using the calculated $$(x, y)$$ pairs. Connect the points smoothly, keeping in mind the piecewise nature of $$y$$ and that the curve will have a 'V' shape due to the absolute value. Add arrows along the curve to indicate the orientation corresponding to increasing $$t. $$Since $$x = 2t$$ increases as $$t$$ increases, the arrows should point from left to right along the curve.

In Exercises 9–20, use point plotting to graph the plane curve described by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x = 2t, y = |t − 1|; −∞ < t < ∞

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주요 개념

Parametric Equations

Graphing Parametric Curves

Orientation and Direction of Parametric Curves