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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.

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02:48

Wen Zheng

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

16:57

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

01:59

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

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Match each pair of graphs …

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Graphs of Parametric Equat…

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Match the set of parametri…

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Match the parametric equat…

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Match the graphs of the pa…

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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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