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By Harley Flanders; Justin J Price

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L Ob). • Two more rational functions are graphed in Fig. glance at Fig. I la shows that the lines x = l, x = - l, and y = l play a special role. These lines are called asymptotes of the graph. In general the line x = a is called a vertical asymptote of the graph y = /(x) if I/(x) I - oo as x - a. non-vertical line L is called an asymptote of a graph if the vertical distance between the line and the graph approaches 0 as x - ex: or x - - oo (or both), for example, the line y = l in Fig. l Ob. 1 1 A 11.

48 1 . \'. (b) If x and y are interchangeable in the 2 4 6 8 10 center (5, 12), radius 13 center ( - 2, - I), radius I center (3, 3 ), through ( - 2, -4). center (I, 2� tangent to x-axis diameter from (-2, -3) to (4, I ). equation y = f(x), then the graph is symmetric in the line y = x. EXERCISES Write the equation or the circle 1 center (I, 3), radius 6 3 center ( -4, 3), radius 5 S center (I, 5), through (0, 0) 7 center ( - 5, 2), tangent to y-axis 9 diameter from (0, I ) to (3. 3) Write the equation for the most general circle.

F(x) = (x - ri ) · · · (x - r,, ). It is important how many times each factor (x - r1) occurs, so we write r, < '2 < . . < r, • to show clearly each zero r1 with its multiplicity m1 • 8. Polynomials and Rational Functions 37 x Ff&. 3 Ff&. 4 Graph of y = (x - r)2(x - s� r>s Graph of y = (x - r)(x - s)(x - t� r

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