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Thinking Task # 2 Rational Functions: Total 11 marks Given the following two functions shown below. The graph in green is y = f(x) and the graph in blue is y = g(x) -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 (-2.5, -0.556) -8 -7 6 -5 4 3 2 Pr --2 -3 -4 -5 -6 -7- 3 4 5 6 7 8 Determine the intervals on x where f(x) > g(x). Your solution must be entirely algebraic. Simply reading the intervals off of the graph will result in a mark of zero. Note: The horizontal asymptote for y = f(x)is y = 1 and the vertical asymptote is x = -7 The horizontal asymptote for y = g(x) is y = -1 and the vertical asymptote for y = g(x) is x = 2
2. A function f(x) has the following properties. a. There is a hole at x = b. There are two zeroes. One zero occurs when x = 4 c. The equation of the horizontal asymptote is y = 1 d. The equation of the vertical asymptote is: x = e. The function passes through the point (0,2) Determine the equation of the rational function and state the 2nd zero.
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