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Changing b results in a reflection over the y-axis. Changing a results in a larger graph with a longer radius all around. The sine of the graph is shifted because of the differing starting points and outputs of sine at the same values.
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The Third
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Changing a reflects the graph over the y-axis. It also affects the radius and size of the graph, higher a values enlarge the graph. The sine of the graph is shifted because of the differing starting points and outputs of sine at the same values.
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The Fourth
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Enlarging a results in a smaller graph, while shrinking a results in a larger, more scattered arrangement. It affects the radius and the center as well. The variable, b, affects how many curves are present in the cardioid(s) at the center.
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The Fifth
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The variable, k, affects the magnitude and size of the graph. As k grows, the graph becomes much wider and more expansive. Variable a affects the starting point of the graph on the x-axis. However, when the a slider is brought on the negative side of zero, the line flips along the line y=x. With a at zero, the line is not existent because zero times the rest of the equation yields zero.
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