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P.1 Graphs and Models I’m so to be in Calculus!!!

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Sketching a Graph by Point Plotting Sketch the graph of y = x 2 - 2 x y -2 0 1 2 3 2 -2 2 7

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Finding x- and y-intercepts

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Find the x- and y-intercepts of the graph of y = x 3 - 4x To find the x-intercepts, let y be zero and solve for x. 0 = x 3 - 4x This factors into? x(x - 2)(x + 2) = 0 x = 0, 2, or -2 the graph has the three x-intercepts: (0,0), (2,0), (-2,0) To find the y-intercepts, let x = 0. y = 0 3 - 4(0) This produces y = 0. So, the y-intercept is (0,0).

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Symmetry y-axis x-axisorigin (x,y)(-x,y)(x,y) (x,-y) (x,y) (-x,-y) (-x,y), (x,-y), and (-x,-y) are the key points in determining symmetry.

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Check for symmetry with respect to both axes and the origin. Ex. 4 xy 3 + 10 = 0 Plug in the three ordered pairs. If you can get it to look like the original equation, it has that symmetry. y-axis (-x,y) (-x)y 3 + 10 = 0 -xy 3 + 10 = 0 Is this, or can we get this to look like the original? No. x-axis (x,-y)x(-y) 3 + 10 = 0 -xy 3 + 10 = 0Not like the original. origin (-x,-y) (-x)(-y) 3 + 10 = 0 xy 3 + 10 = 0 This graph has origin symmetry.

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