PrecaIcuIus(H)
Determine the asymptotes for each function.
12. y=—--
(x+1)
±
:1:1:__
—,—
—
Ii
V
H---v
:1::::::::::
Determine the values of x for which a hole appears in the graph of each
function.
13
—
(x—3)(x+5)
(x+5)(x—1)
2 + 3x 28
x
2 + 28x
11x
—
14. y=
—
Determine any horizontal, vertical, or slant asymptotes in the graph of each
function.
15.y=
17,y=
x
16. y=
x+x-6
3
3x
—
2x + 1
—
21. vertical asymptote at x
=
22. vertical asymptotes at x
3 and x
=
4,
=
—
3
3x
+ 4x +4
—
Create a function of the form y
=
x
18. y=
2
2x
23. holes at x
2
llx+30
1(x) that satisfies each set of conditions.
hole at x
—5 and x
—7, resembles y
0
1, hole at x
=
x
=
-1
Graph each rational function.
24. v
=
-
3
x+2
25.
-
(x +2)(x— 2)
27.
30. 3’
=
31. y
3
36. v
-
39.
28. y
x-x
x
=
(x
=
x
,
1—x
y
=
x—5
x+1
=
x
-4
y
=
—
(x
x2
-5
3)(x ± 1)
32.
+ 3x
s[
x—1
-2
29. y
(x
=
26.
35.
>‘
=
x(x
—
1)
+ 3x
‘
—
4
=
—
Graphy=
37.
2(x
y
-x
=
38.
,
y
x—1
=
—--—
x—4
x + 1)
3x
(
2
1)
2)(x
—
—
Louis was baby-sitting his neighbors two children and decided to
take them to the park. The children wanted to play on the seesaw. When they
got on the seesaw, the older child was too heavy for the younger one. Louis knew
that if the older child sat closer to the center of the seesaw, it would work better.
The equation relating the two weights and the distances from the center of the
1 is the distance
1 is the weight of one child and d
, where w
d
2
1d
1 = w
seesaw is w
weight and
the
are
2
w
and
2
d
and
of that child from the center of the seesaw
distace for the other child.
40. Amusements
I-.
..
.-
-
$
..
-
Suppuse th children are balanced on the seesaw. One child weighs 30 pounds
and sits 6 feet from the center of the seesaw. Write a rational function to find
the weight of the other child.
b. Graph the function in part a.
c. If the older child weighs 45 pounds, how far must she sit from the center of
the seesaw?
d. Make a general conjecture about the relationship of a person’s weight to the
distance from the center of the seesaw in order to make it work properly.
a.