222 42 CHAPTER 1 FUNCTIONS AND MODELS MIT 1.3 Exercises bon 6) bms 76211 DAMAX 1. Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (b) Shift 3 units downward. is the intersec x2 is given. Use transformations to 6-7 The graph of y = 3x create a function whose graph is as shown. (d) Shift 3 units to the left. (f) Reflect about the y-axis. Shaip to nism 1.5T y= 3x-x (a) Shift 3 units upward. (c) Shift 3 units to the right. (e) Reflect about the x-axis. (g) Stretch vertically by a factor of 3. (h) Shrink vertically by a factor of 3. 2. Explain how each graph is obtained from the graph of y = f(x).\' (a) y = f(x) + 8 (c) y = 8f(x) (e) y = f(x) - 1 (b) y = f(x+8) (d) (f) y = 8f(x) y = f(8x) 0 red izum sw boniteb sd of 7, 10 6. [0] Invisini 3-2015 Srl 3. The graph of y = f(x) is given. Match each equation with its graph and give reasons for your choices. (a) y = f(x4) (c) y = f(x) (b) y = f(x)+3 = -1) (d) y = f(x+4) 0 2 5 X 7. 3 x domain -4 -1 0 x -1 -2.5 (e) y = 2f(x+6) TITO+ -6 (2) 3. I for halevi 3 (.0] 21 to niemob or = 2 sin x related to the graph of 8. (a) How is the graph of y y = sin x? Use your answer and Figure 6 to sketch the - diod nodw bsnitsb ali graph of y 2 sin x. al broosa all bus S (b) How is the graph of y = 1 + x related to the graph of = - visini berat pero sob story = x? Use your answer and Figure 4(a) to sketch the -3 0 4 3 6 graph of y 1 + x. gmos stb sols of sldiazoq a X ollol not be nodi griyo 12it bnuot ai 9-24 Graph the function by hand, not by plotting points, but by -3 (5) (())=((dp) starting with the graph of one of the standard functions given in Sec- tion 1.2, and then applying the appropriate transformations. 1 9. y = 10. y = (x-1) 4. The graph of f is given. Draw the graphs of the following functions. (a) y = f(x) - 2 (c) y = -2f(x) (b) y = f(x 2)\ / p = 0 (d) y = f(x) + 1 x+2 11. y = x 12. y = x + 6x +4 MOITUJ02 13. y=x-2-1 14. y = 4 sin 3x = y 2 siqmiz omi noi ordios maginos blind of nonizoqmo 17. y = (1 - cos x) Odahomeass of olds ad o lutear asilo kiauluso ni 19. y = 12x slarinxe go x 2500 2 ===2 X 18. y=12x +3 20. y= |x|-2 15. y = sin(x) ed. 16. y 5. The graph of f is given. Use it to graph the following functions. (a) y = f(2x) (c) y = f(x) Lbe izid (b) y = f(x) (d) y = f(x) w 02 supa vilen b 11 0 1 Homework Hints available at stewartcalculus.com 21. y = |x2| 7.) 200 (7) novi x)200 23. y= |x-102 1 TT 22. y= tan x 4 24. y= |cos TX | 25. The city of New Orleans is located at latitude 30N. Use Fig- ure 9 to find a function that models the number of hours of daylight at New Orleans as a function of the time of year. To check the accuracy of your model, use the fact that on March 31 the sun rises at 5:51 AM and sets at 6:18 PM in New Orleans. SECTION 1.3 NEW FUNCTIONS FROM OLD FUNCTIONS 43 26. A variable star is one whose brightness alternately increases and decreases. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average brightness (or magnitude) of the star is 4.0, and its brightness varies by 0.35 magnitude. Find a function that models the brightness of Delta Cephei as a function of time. 5T 27. (a) How is the graph of y = f(|x|) related to the graph of f? (b) Sketch the graph of y = sin |x|lov pasioni Isubstg (c) Sketch the graph of y = |x| sged to doing or do1922 (d) 28. Use the given graph of to sketch the graph of y = 1/f(x). Which features of f are the most important in sketching y = 1/f(x)? Explain how they are used. slummot & to boring av all Hot Now Yo 1961 41-46 Express the function in the form fog. 41. F(x) = (2x + x2)4 43. F(x)= x 42. F(x) = cosx x 1+x l (d) tan t AZ 1+ 3x 28 9107 44. G(x) = 45. v(t) = sec(t) tan(t) bo46. u(t) 1 + tant (abno se ni) 15mil the function in the form fogo h. dai V 11 (d) 47-49 Express the function in the form 47. R(x) = x - 1 148. H(x) === 2+ |x| ai sgilov s si ti unioni (t)V bs abos? W naslov or to dqsig od dots (5) Lami to no bumul ai doliwa gd\mal 0 to basqa s is gnivoin ai qida A .22 49. H(x) = sec(x) 2928 i bode mont mal ai gida orTanilsToda noon 16 szod id + zim 1 (x)\ anoitsuo nomad/ bra Pored offtain numb .02 11 noitonul sila oto padets or in the domam off, or if figyel paladwThe machine conne Wabo S he machine draws the 50. Use the table to evaluate each expression. (a) f(g(1)) qida (b) gf(1)) pl(d) g(g(1)) ib or 22919 (s) to (e) (gof)(3) (c) f(f(1)) (f) (fog)(6) the an X 1 2 3 4 5