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7.4a Linear Reciprocal Functions What is a reciprocal? A product of a number and its reciprocal always equal to 1. 1 The reciprocal of n is n , if n ≠ 0 because n x 1 n =1 Find the reciprocal of the following numbers: 10 5 1 ½ 0 -¾ -1 -20 -100 • What do you notice when you take the reciprocal of numbers greater than 1 or less than -1? • What do you notice when you take the reciprocal of numbers -1 < x < 1 ? Comparing Graphs of a funtion and its reciprocal Let's compare the two graphs y = x x y=x y=1/x -10 -5 -2 -1 -0.5 -0.25 -0.01 0 0.01 0.25 0.5 1 2 5 10 Ch7(Absolute Value) Page 1 and y = 1 x In general, to graph a reciprocal function 1 : f(x) 1. Graph y = f(x) 2. Draw the vertical asymptote(s). This is the x-intercept of f(x) because f(x) = 0, and reciprocal of zero is undefined. 3. Draw the horizontal asymptote. The value y approaches as |x| approaches infinity. 4. Label the invariant points. When f(x) = 1 or -1 5. Use asymptotes and invariant points to sketch. (Big -> Small) When f(x) > 1, the reciprocal function approaches the horizontal asymptote (Small -> Big) When 0 < f(x) < 1, the reciprocal function approaches the vertical asymptote Example 1: Given f(x) = ½x - 4 a) Determine y= b) Determine the horizontal and vertical asymptotes. c) Graph Example 2: Graph y = 1 x-3 Ch7(Absolute Value) Page 2 Assignment: Sec. 7.4a p403 #1ab, 2ab, 3ab, 4, 5ab, 6a, 7, 9ad Check question 7a: It should be f(x) = x - 4 (some texts have it wrong) Ch7(Absolute Value) Page 3