Page 63 - Math SL HB Sem 1

,,r_
Functions ard Relations CH._\pTER
.\s was rhe case rbr the e\ponentiar antj iogarithmic functions. ihc nodzontai ard verdcai
asymgtotes oi tlre basic tuncrion
/{r) = , - O can al;o be reloc:lted . \\,e summarise rhese
1
resulls nou':

Case 2: tt = -2

wirh n = ? rve have the equation
- this graph has a shape known as a
truncus

Thc reason for its name becomes obvious once we sketch its graph _ ir looks like rhe trunk of a
tree. As before, we can make use of a table of values and plot its graph, however, this time lve list
the properties ol this lunction and its graph:
l- Function is undefined at.r
= 0
,.\s)/mPtores are: venicil,.r
= 0 I |
-;,*t
horizontal, y = Q I '-l "ii i (i .)
l I
lle :;aph is symmetrical about the.),_aris.
I I
,
I
\il.i)
.-----
\Vc cirl l-ro lrakc thc following obse.\,ations:

I Tir, tr.rph ot r,-,- l;;,r-o is irlenrrcai to r,=
I 1 X)' ; burnro;erl (.r,njr" rothr
'i<,,, ,rr(] c,r nuj u \enical asymptote at.{ t.
) =
fh':gr'rl lrcl , -,-1r,, * .0 I r::r::,., .r
t,: \ k:: isrdentrcrl ro, .,.. ,,.r. .., ih.. ,ri,
.l
'r:l \o h,r\ a re;ti(alasvmo(oic
al .r _ _.{

t- l6