APPM 1340 Midterm: appm1340fall2017exam2_sol
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Fall 2017: [12 pts] in your bluebook, write t if the statement is true and write f if the statement is false. Then the graph of f must cross the x-axis somewhere between a and b. Solution: (a) false x2 = |x| (b) true rational functions are continuous on their domains. (c) false consider f (x) = |x|. 2x3 2x2 4x (a) write the domain of g(x) in interval notation. (b) find all horizontal asymptotes of g(x). Justify your answer using limits. (c) find all vertical asymptotes of g(x). For the various parts of this problem, it is useful to consider other forms of the function: factored, and rewritten (assuming x 6= 0) after multiplication by (1/x3)/(1/x3). 2x(x + 1)(x 2) x + 6 x2 x 4. 2 2 g(x) = x2 (a) from the factored form, the zeros of the denominator are 1, 0, 2.