Mathematical Investigations III
Name
Mathematical Investigations III
The World Upside Down
Review and Practice
1.
Write an equation for a rational function that reduces to a linear function for all x ≠ –5,
has a "hole" in the graph at (–5,8) and a y-intercept at –7.
2.
Sketch the graph of the reciprocal of the
function shown to the left. Be sure to
indicate important features.
3. Write the equation for the rational
function sketched to the right.
y
1. 5
-2
Rats 8.1
-1
2
4
x
Rev. S05
Mathematical Investigations III
Name
Graph each of the functions given. Label all key features, including asymptotes, holes,
intercepts, where the graph crosses a horizontal asymptote, and other important points.
4.
y

2 x4
y

2
25
x  3x  2
x
-5
7
-20
5.
y
x2
x2  1
y
5
x
-5
5
-5
Rats 8.2
Rev. S05
Mathematical Investigations III
Name
6.
y
y
   
2 x  6x  2x  3
3 x 1 x  4 x  6
15
x
-7
5
-15
y
7.
x  2x  7
y
2 x  1
15
x
-5
8
-15
Rats 8.3
Rev. S05
Mathematical Investigations III
Name
Choose your scale appropriately on these.
8.
9.
y



x x5

2
3 x 1 x  2

x 2 (x  2)(x  3)
y
x2  1
Rats 8.4
Rev. S05
Mathematical Investigations III
Name
10.
Find the equations of all asymptotes of each of the following.
3x 2  8x  2
a.
h(x) 
x3
b.
11.
j(x) 
x 3  5x 2  6x  1
x2  x  2
Write an equation of a rational function, R(x), with the following characteristics:
zeros at 3 ± 4i, a bounce point at x = 2, a horizontal asymptote at y = 0.5, and
a vertical asymptote at x = 0 where lim R(x )   .
x0
Rats 8.5
Rev. S05