401 Relating Concepts For individual or collaborative investigation (Exercises 119 –128) Consider the following “monster” rational function. ƒ1x2 = x4 - 3x3 - 21x2 + 43x + 60 x4 - 6x3 + x2 + 24x - 20 Work Exercises 119–128 in order. 119. Find the equation of the horizontal asymptote. 120. Given that -4 and -1 are zeros of the numerator, factor the numerator. 121. Given that 1 and 2 are zeros of the denominator, factor the denominator. 122. Write the quotient for ƒ with numerator and denominator in factored form. 123. (a) What is the common factor in the numerator and the denominator? (b) For what value of x will there be a point of discontinuity (i.e., a hole)? 124. What are the x-intercepts of the graph of ƒ? 125. What is the y-intercept of the graph of ƒ? 126. Find the equations of the vertical asymptotes. 127. Find the point(s) of intersection of the graph of ƒ with its horizontal asymptote. 128. Sketch the graph of ƒ. Chapter 3 Quiz (Sections 3.1–3.5) 1. Graph each quadratic function. Give the vertex, axis, domain, range, and largest open intervals of the domain over which the function is increasing or decreasing. (a) ƒ1x2 = -21x + 322 - 1 (b) ƒ1x2 = 2x2 - 8x + 3 2. (Modeling) Height of a Projected Object A ball is projected directly upward from an initial height of 200 ft with an initial velocity of 64 ft per sec. (a) Use the function s1t2 = -16t2 + v 0 t + s0 to describe the height of the ball in terms of time t. (b) For what interval of time is the height of the ball greater than 240 ft? Round to the nearest hundredth. Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ1k2. 3. ƒ1x2 = 2x4 + x3 - 3x + 4; k = 2 4. ƒ1x2 = x2 - 4x + 5; k = 2 + i 5. Find a polynomial function ƒ of least degree having only real coefficients with zeros -2, 3, and 3 - i. Graph each polynomial function. Factor first if the polynomial is not in factored form. 6. ƒ1x2 = x1x - 2231x + 222 7. ƒ1x2 = 2x4 - 9x3 - 5x2 + 57x - 45 8. ƒ1x2 = -4x5 + 16x4 + 13x3 - 76x2 - 3x + 18 Graph each rational function. 9. ƒ1x2 = 3x + 1 x2 + 7x + 10 10. ƒ1x2 = x2 + 2x + 1 x - 1 CHAPTER 3 Quiz
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