MATH 1710-005 Homework 9: Rational Functions and Asymptotes - Prof. Tsz Chan, Assignments of Pre-Calculus

Download MATH 1710-005 Homework 9: Rational Functions and Asymptotes - Prof. Tsz Chan and more Assignments Pre-Calculus in PDF only on Docsity! MATH 1710-005 Homework #9 (due 4/10 Fri) Please show your works. Section 3.5 1. For the following rational functions, nd all the asymptotes. Then with the help of a table, sketch a graph. Be sure to label all the asymptotes and the x- and y- intercepts. Afterwards, you can check your answer with your graphing calculator. (a) f(x) = 2x 1 3x+ 4 : (b) g(x) = 3x+ 3 2x2 5x 3 : (c) h(x) = 5x3 x2 + x 1 x2 x 1 : 2. (a) Find a rational function with vertical asymptotes x = 4, x = 5 and horizontal asymptote y = 3. (b) Find a rational function with vertical asymptotes x = 4, x = 5; horizontal asymptote y = 3; and y-intercept (0; 2). Hint: Try to add a constant to the numerator of your answer in part (a) so that when x = 0, the whole expression has value 2. Section 3.6 3. Solve 2x3 + 6  5x2 + x. Hint: Move everything to one side and factor. Then set up a table. 4. Solve 3x+3 2x25x3 > 0. Hint: You may use your answer in question 1.