P
P
i
i
e
e
c
c
e
e
w
w
i
i
s
s
e
e
D
D
e
e
f
f
i
i
n
n
e
e
d
d
F
F
u
u
n
n
c
c
t
t
i
i
o
o
n
n
s
s
Piecewise defined functions can easily be graphed on the calculator by breaking them up into their
components.
⎧
sin
()
; x <−2x
⎪
⎪
()
=
⎨
x
+
2 ;
− ≤ ≤
1
For example:
fx 2 x
⎪
2
⎪
(
x
−
2
)
−
1 ; x
>
1
⎩
Using the Function aplet, we enter three separate component functions.
You can obtain the inequality signs
from the
CHARS menu.
F1(X)=SIN(X)/(X<-2)
F2(X)=(X+2)/(-2≤X AND X≤1)
F3(X)=((X-2)2-1)/(X>1)
The calculator evaluates the domain as either true (1) or false (0)
for each value of x. When it is zero (outside the domain) then
dividing by this value causes the function to become undefined and
consequently not be graphed. Inside the domain it has no effect.
Note:
The AND is available on the keyboard above the button.
S
S
e
e
q
q
u
u
e
e
n
n
c
c
e
e
s
s
a
a
n
n
d
d
S
S
e
e
r
r
i
i
e
e
s
s
Through the Sequence aplet the hp 39gs & hp 40gs provide very flexible tools for the investigation of
sequences. These can easily be adapted to investigate series as well. Information and worked examples of
using the calculator for evaluation of sequences and series can be found in the chapter “The Expert –
Sequences & Series” on page
102.
One of the common errors that students make when using the Solve aplet with GPs is to try to solve for
solutions which do not exist. For example, a student will try to solve for
N in T=A*R^(N-1) with A=50,
R=0.75 & T= -2. The result will be firstly that the calculator will seem to
freeze while it tries to find a solution which can only be approached
asymptotically.
Finally the calculator will give the result as shown right. The problem is
that students will tend to misinterpret it as being
N=10, when in fact it is
simply that the calculator has gone as far along the positive x axis as
possible and stopped at
MAXREAL of 11
500
(see second screen shot).×
It is recommended that the teacher should deliberately provoke this error
and follow with class discussion.
322
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