2.2 Graphs of Equations in 2 Variables

2.2 Graphs of Equations in 2 Variables - x and solving for...

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2.2: Graphs of Equations The graph of an equation is the set of all points that satisf y the equation. For two-variable graphs, to find some of the points, substitute some numbers for x and solve for y . Be sure to find sufficient points to show the pattern of the graph, so that an y viewer will see the rest of the graph as an obvious continuation of what is actuall y there. This is called the complete graph . For non-linear equations, checking for intercepts and s y mmetr y reduces the number of points needed to find the complete graph. The coordinate of a point at which the graph touches or crosses the x -a x is is the x -intercept and is found b y substituting 0 for y and solving for x . The point at which a graph touches or crosses the y - a x is is the y -intercept and is found b y substituting 0 for
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Unformatted text preview: x and solving for y . A graph is symmetric to the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph. It is symmetric to the x-axis if for every point (x, y) the point (x, -y) is also on the graph. It is symmetric to the origin if for every point (x, y) there is also a point (-x, -y). (1) Given the point (4, -2), find the point that is symmetric with respect to the: x-axis y-axis origin (2) Tell whether the given points are on the graph of the equation x 2 + 4y 2 = 4: (0, 1) (2, 0) (2, ) List the intercepts and test for symmetry: Intercepts Symmetry: does (x, y) = x-y-x-axis (x,-y) y-axis (-x, y) origin (-x,-y) 3 y 2 x 4 = 0 4 y = x 3- 8 5 4x 2 + y 2 = 4 6 2 y x =-7 y= -x 2 + 3 8 y = x...
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