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Match the graphs of the parametric equations $ x = f(t) $ and $ y = g(t) $ in (a)-(d) with the parametric curves labeled I-IV. Give reasons for your choices.

(a) Graph III(b) Graph I(c) Graph IV(d) Graph II

02:48

Wen Z.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

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So looking at the given graphs, we want to match them to their functions and we have the parametric equations. So we see the X. Is going to equal FFT and why is going to equal GFT? So we need to consider how um exchanges with an increase in T independently as wide increases or Y changes as X increases. Um So we're going to label the graphs based on the answer is so we see that for parquet, if we look at t increasing and see how X is going to behave separately and see how y is going to behave separately, we see that this is going to be the graph of three. Ben for part B doing the same thing, we get graph one is our answer part C. We get graph four. And then for part B we get graph too. Yeah. So that's gonna be our final result.

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