Read
- Chapter 3 of the textbook (https://openstax.org/books/algebra-and-trigonometry/pages/3-introduction-to-functions)
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Consider the equation x^2 + (y-2)^2 = 1 and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”.
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For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation x^2 + (y-2)^2 = 1, if and only if, (x, y) R (0, 2)”.
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Does this equation determine a relation between x and y? Can the variable x can be seen as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y= h(x)? If these are possible, then what will be the domains for these two functions? What are the graphs of these two functions?
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Are there points of the coordinate axes that relate to (0, 2) by means of R?
Be sure to use in-text citation and provide references for your sources, including textbooks.
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