program proyides exercses related to yo dion when petorming exercses W you exper medbridgego.com STO pred ABLE TABLETS SUM RCL Access Code a%e Actual Size SOENTA 2/90 8ERIS wre dreft POLY SUE 175 Rational Functions in. 2.6 2.6 Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. 1 in. 2.28 Vocabulary: Fill in the blanks. 1. Functions of the form f(x) = N(x)/D(x), where N(x) and D(x) are polynomials and D(x) is not the zero 2. When f(x)→±0 as x→a from the left or the right, x = a is a_ 3. When f(x) →b as x→±00, y = b is a. 4. For the rational function f(x) = N(x)/D(x), if the degree of N(x) is exactly one mo From Figure 2.28, you can ted area inside the margins o find the minimum area, s of just one variable are called of the graph of f. of the graph of f. than the degree of D(x), then the graph of f has a by (48 +2x) Skills and Applications Finding the Domain of a Rational Function In Exercises 5-8, find the domain of the function and discuss the behavior of f near any excluded x-values. х tility to create a table of (48 + 2x)]/x beginning minimum value of 8 and 9, as shown in nimum value of y, to co begin at x = 8 and х 4s 25. g(s) 26. f(x) = (x - 2)2 s2 + 4 Зx 2x 27. h(x) = 28. g(x) x2 + 2x - 3 x2 - 3x - 4 5x 6. f(x) х — 4 x2 - 16 5. f(x) = 3x2 29. f(x) = 30. f(x) x2 - 1 e of yı Occurs when e corresponding value dimensions should be hes. 2x 8. f(x) = x - 36 12 1 x2 - 4 31. f(t) = 32. f(x) = x2 - 1 7. flz) = t - 1 Finding Vertical and Asymptotes In Exercises 9-16, find all vertical and horizontal asymptotes of the graph of the function. Horizontal x2 - 4 x² – 25 33. f(x) = 34. f(x) x2 - 3x + 2 x2 – 4x – 5 5(x + 4) x2 + 3x Y1 35. f(x) = 36. f(x) = x2 + x – 6 x² + x - 12 87.961 87.949 87.943 87.941 87.944 87.952 87.964 2x2 - 5x - 3 10. f(x) = 37. f(x) : (x – 2)3 x - 2x? – x + 2 9. flx) = 3 - 7x x² - x - 2 x³ – 2x2 – 5x + 6 12. f(x) 38. f(x) 3 + 2x 11. flx) = 4x2 14. f(x) : Matching In Exercises 39-42, match the rational function with its graph. [The graphs are labeled (a)–(d).] %3D x2 - x 13. f(x) = - 4x2 + 1 ² - 3x - 4 2x2 + x - 1 16. f(x) (a) (b) x² + x + 3 15. f(x) = Graph of a Rational 2 HO Sketching the Function In Exercises 17–38, (a) state the domain of the function, (b) identify all intercepts, (c) find any vertical or horizontal asymptotes, and (d) plot additional solution points as needed to sketch the graph of the F1 3 5 4 6 n (page 166). Example 1. ne graph tical and ple 2. (d) (c) rational function. 1 18. f(x) fle) = 17. flx) 3 x + 1 3. 4. -4 ). For ples 3-6. -1 19. Alx) = * + 4 20. g(x) -3x 2x + 3 n has a 22. P(x) 21. C(x) 40. f(x) 39. f(x) = h of a -- 2t 3x 2x2 41. f(x) = 23. flx) x² +9 42. f(x): 24. f(t) %3D solve (x+2)2 x2 - 4 PON OR OFFERS 4+ NTIFIC