k E 'i
Name
PreAP Algebra 2
Test Review - Rational Function Attributes
Analyzing Rational Function Attributes
50
far in basketball season, during games Charlie has shot 30 free throws. Unfortunately, she has only
,ade 13 of t~em. Up to this point, what is her stat for percent of free throws made?
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'3 0 ::::
3.3,) " I
3, ?;
After such a poor start, Charlie gets some advice from the coaches and practices daily. If she does not
miss another free throw for the remainder of the basketball season:
I
'+
o, '+
I
How many consecutive
# Extra
'70
free throws will she need to make before her percent reaches 80% ... 90% ... 100%?
Fraction Made
Decimal
Consecutive Free
Throws Made
Riqht Now
4-
0,'1 ~ .,
.!f.l'l
Sketch the graph of this
relationship in the given
window.
Percent
'3,? '/1)
# Extra Consecutive
)
After how many consecutive free throws will Charlie's percentage
reach 90ol??
2. When will the percentage
,
3. When will it reach 100%?
I. Transformations
) 4-0
+y~
+t1VbW
reach 80%?
S
n..Q.v~('
from an equation:
[ex) =
1. a. Graph the equation
_1_ -
x-3
2
2. a. Graph the equation [ex) = -
'f... -::: :3
b Vertical Asymptote:
b. Vertical Asymptote:
c. Horizontal
Asymptote:
'1 -=- -
d.Domain:
{KE:IRI
Xi3~
d .Domain:
y/-2..1
e Range:
fycIRI
e.Range:
c. Horizontal Asymptote:
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((-
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..•.
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>
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)
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r-r- I-
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II
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~
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1_
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•.......
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x
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i.:X
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00)
100
~
,
_1_
x-I
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'X:::.
y
y
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Free Throws
u ( 3)
3
00)
~)
+3
..
.
x.
(
II. Transformations
CL.
\) -=-
,l(-h
-~.-.-----
J.
I -
from a graph:
+K
-f
_ ..
4.
-+----1
_._\
(
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i
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,
--.
-,
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.
:..-J-,
.
X '1
--t-- ,)
~ i1--~~
!
1
-
J'
• .J.
-3
,'2
-I
(I) 0)
\
+
o -:;.~
)-2
-,{
-::.
_._~~.__
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tL.:: I
-/
)( :;.. 2..
Asymptote:
_,I
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(
{t1
~
CL~-/
a. Write the equation
~
=. 'X_
b. Vertical Asymptote:
X.
.::t
I
I ~ X-2. + /
a. Write the equation
b yertical
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j
~~::::::::::::I----1_
--------'-"-'M---t-r-t--+---<
-i
j
- I
I'
:--2 -::.. 1=2-~
I-=-.:T
II-
'2.. )
_/
z,
3
-=- 2
1
c.HorizontaIAsymptote:
d. Domain:
e. Range:
t
f~
IR ( X
E
r
~::::-
*
c. Horizontal Asymptote:
2- ~
[y e ~ I y =1 '. ~
~
-=-.-
3
l.) U ( 2) t:O)
d .Domain:
"D ~ (-
e. Range:
R: (- ~ -3) V (-
(0)
3 ) -po)
I. Find Vertical Asymptotes, Holes, Zeros from equations:
=
1_ [ex)
(X+4)(X-l)
(x+Z)(X+l)
2. [ex)
~+~
=
'/,.-::-1
'f... -;.. -'i..)
NO~e:
Holes
Zeros
V.A
Holes
(~y)o)(I)O)
Zeros
(x+3)
x(x-z)
3. [ex)
-3)
x-3)
~~
~ (!.~2-)
V.A.
(~+3Y~+2-)
= xZ+sxt6
4.
xL36
('/-..-"')(:~f-~)
.3
K-=O
)
'A -:. ~ I X 0;
V. A
X::2
(3 ) 2.. )
(_ ~ ) 0)
V.A
- (.,
NON ~
Holes
Zeros (-
'3> I
'f -::.- '-
Holes
0) / -2,) 0 )
Zeros
X ::
(0) 0)
IV.Finding Horizontal Asymptotes and y-intercepts from equations:
1)-:. "1. [ex) = 3xZ+Zx-S
I\l:."l.
H.A.:
y-int:
'I":.:.
(0
I
xZ+l
3
-5')
f'J':.2
:::..? 2.
I
[ex)
J-LA.:
y-int:
=
y
Z
Zx +6x+4
X3+XZ+X
=. 0
NO tJ€
;:10
3. [ex)
'D::'f
= 9xZ-ZS
L
x 16
~
-II,
'f -::.0
y-int: (0) %)
H.A.:
4. [ex)
=
H.A.:
y-int:
3x2+ZX
x2+4x+3.3
"2-
::- ~
'I -;::
3
(0) ())