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# Class Note for MATH 1310 at UH 2

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

Seclinn 52 Du ni nn and anh unhe Nzlunl Expunm zH unc nn Page 1 hr 9 De nition and Graph ofthe Natural Exponential Function The exponehtrai fuhetror wrth base 2 fx gx rs eauedthe natural expnhehtial functinn The numbere rs ah rrratrorrai number and rs de ned as the value that Hih approaches as h becomes large To ve deermal p1aees e e 2 71m The gaph offx e rs shown below doman 70000 7 range app horizontal asymptote y 0 rteoasreem Example 1 Sketeh the graph of the function fx eex by startahg from the graph ofy State the domain range and asymptote Snllltinn tn Example 1 To sketeh the graph of the fuhetrOhr 2 re eet the graph ofye m the xraxxs Seclinn 52 Dr ni nn and anh unhe Nnunl Expunm zH unc nn Page 2 hr 9 duck h t th we The domam ls 70000 The range is exam The honzonta1 asymptote lsy 0 Example 2 Sketeh the graph of the functionx 22X by makmg atable ofvalues and plothhg pomts Idehttfy the domam range and asymptote Snllltinn tn Example 2 Make atable of values to determan pomts on the graph ez 14th a uz7 7 222 71 neueze zaznu ehze n 1a 2a 1 f12a 2a 44 212 m 2 12 22 1472 Seclinn 52 neruriu39urr m anh nfdlz Nzlunl Expunm leunc nn Pig 3 ul 9 Sketch the graph domam 70000 range 000 horizontal asymptote y 0 Example 9 True or False7 7 gt1 Do not use a calculator to determan the answer e Snlntinn m Example 2 lt3 smeee 271828 The answens true Seclinn 52 Delmam and anh unhe Nzlunl Expunm leunc nn Page o hr 9 Example 4 Sketch the graph of the fuhehohr 72 8 Do not plot polnts but lnstead apply transformations to the graph ofthe fuhehoh y 2X Identlfy the olorharh range and asymptote Snlutinn m Example 4 Begln wlth the graph ofy 2X shown below To show the graph othe functionx 72 8 rst re ect the graph of X m the Kraxls y Seclinn 52 Du ni nn m anh arm Nzlunl Expunm le unc nn Pig 5 ul 9 Now shm upward 8 umts fx 72 8 domam 70000 range 7008 horizontal asymptote y 8 Example 5 Seclinn 52 Dr ni nn and anh unhe Nzlunl Expunm leunc nn Page a at 9 Sketch the graph of the fuhehohr ex 7 3 Do not plot polnts but lnstead apply transformations to the graph ofthe functlon y 2X Identlfy the olorharh range and asymptote Snlutinn m Example 5 Begln wlth the graph ofy 2X shown below To show the graph ofthe fuhehohr e 1 73 rst shrmhe graph of y 2X to le 1 null Seclinn 52 Du ni nn m anh arm Nzlunl Expunm le unc nn Pig 7 ul 9 Now shx downward 3 umts x EM 1 7 3 domam 70000 range 7309 horizontal asymptote y Exercise Set 52 The Number e Answer the following 1 State the value of e correct to three decimal places Compute the following with a calculator Round your answers to three decimal places a e0 b e c e2 d e3 e t True or False Answer these without using a calculator 3 e2lt9 e2gt4 Jlt2 Jgtl Answer the following 13 Graph fx 2 C and gx e C on the same set of axes 14 Graph fx e and gx 3quot on the same set of axes 15 Sketch the graph of f x e and then find the following a Domain b Range c Horizontal Asymptote d yintercept 16 Sketch the graph of f x 3 C and then find the following a Domain b Range c Horizontal Asymptote d yintercept e How do your answers compare with those in the previous question Graph the following functions by plotting points Round the yvalues to the nearest hundredth Be sure to include any asymptotes on the graph Then state the domain and range of the function 17 18 fx 72a x fx for eH 4 x fx Graph the following functions not by plotting points but by applying transformations to the graph of y ex Be sure to label at least one key point on your graph the transformation of the point 0 1 and show any asymptotes Then state the domain and range of the function 19 20 21 22 mo fx 7e fx ise f x 2f Exercise Set 52 The Number e 23 24 25 26 27 28 29 30 31 32 mo e N e x 7 e271 7 6 x 7e 1 f x iei Y 3 x 7equot 7 2 f x 74H 7 5 x 2W6 7 4 x a 7 3 x 3 2

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