Page 63 - Math SL HB Sem 1

I unctions antl Relatiocs CH-\pTE,:i g

As was the case lbr the a\potential and loearithmic funcdors. ihe oo.lzootai 3nci ve{ticai
asymDtotes oi the basic funcrion l.
-f(-.) - r, O can also bc ielo.Jted. \\e summarise rhese
results norv:

Case 2: n=-2

With n = -? rve have the equarion - this gr-aph has a shape ktolvn as a
Iruncus

Thc reason for is name becomes obvious once we sketch its graph _
ir looks likc rhe trunk of a
tree. As before, we can make use ofa table of values and plotis graph, however, this time we list
the prope(ies of this lunction and its graph:
l. Function is undefined ar_r
= 0-
?- Asymprotes are
venical, -! 0
=
horizontal, _v = 0 +) G.)
_1
1}e g;lph is symmetrical about the \,-axrs

i1.1.)
Wc c;rrt uJro ltrrkt tlrt iolbr,,,ins obscayiliron:

t. lnu,:r.rphol r.=, -l _0
l 'r' ,-.( is;dentrcarr,r r, t'' I
^.)r
nPhi ind s(, itrs J !enicrl asymptotc at.r t.
=
'n.i.:r,rlh cJ , _.-_ _-,.i. -0 jsrdenrrc,l ro, . r LrL i rt
''.,P: i, ri .r iir 1:i,
ai)'J so has a !eilical
asvrnDtote at -r _ _i.

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