Name
Date
Algebra 2 PreAP Review 9.1 - 9.4
Describe the combined variation that is modeled by each formula.
1
3V
1. A  bh
2. h 
2
B
1 
 1 
3.  , 6  and  x,  are from an inverse variation. Find x.
3 
 2
4. Suppose z varies directly with x and inversely with the cube of y when x = 8, y = 4 and z = 3. Find z
when x = 6 and y = 4.
2
that has asymptotes at x = -5 and y = 9.
x
5. Write an equation for a translation of y 
For each reciprocal function, describe the translations and transformations.
6. y 
1
3
x
7. y 
4
x2
8. y 
9. Find the points of discontinuity for y 
8
5
x2
x  11
.
x  9 x  22
2
 x  2   x  3
2
10. Find the vertical asymptotes and holes for the function
4 x3  4 x 2  24 x
Rational expressions. Simplify completely and state any restrictions.
11.
2 x  10
6 x  30
12.
x2  4x
x 2  16
14.
x2  9
x 3
 2
3
2
5 x  17 x  6 x 5 x  2 x
15.
x 2  13x  40 3x  24
x 2  16 x  64 2 x 2  x  55
16.
4 x 2 z 5 16b4 x 7

10a 4b 2
5a9 z
17.
a 4  16 a3  2a 2  3a
a 3  2a 2
4a 2  16
13.
2 x 2  26 x  80
2 x 2  7 x  15
18. Sound intensity is inversely proportional to the square of the distance from the source – the farther
from the source you are, the less intense the sound. Suppose the sound intensity is 30 watts per square
meters (W/m2) at 8 meters. What is the sound intensity at 4 meters?
19. The maximum load a cylindrical column can support varies directly as the fourth power of the
diameter and inversely as the square of the height. A column that is 2 ft. in diameter and 10 ft. high can
support up to 6 tons. If a column is 1 ft. in diameter and 12 ft. high, what is the maximum load it can
support?
20. The force required to keep a car from skidding in a turn varies jointly with the mass of the car m, the
square of its speed v, and the curvature c of the turn. The curvature is the reciprocal of the radius of the
1
turn, k  . Suppose it takes 2800 lb of force to keep an 1800 lb car from skidding at 45 mi/h on a curve
r
with radius of 425 ft. What force is needed to keep the car from skidding at 50 mi/h on a curve with a
radius of 440 ft?
21) The monthly cost C(p) of removing p percent of pollutants from waste byproduct in manufacturing
1500 p
can be modeled by the function C  p  
. A manufacturer decides to spend $28, 500 per month
100  p
for removal of pollutants. What percent of the pollutant can the manufacturer expect to remove from the
waste?
22) Write a rational function that has a vertical asymptote when x = 2 and a hole when x = - 3.
Graph each function.
23) y 
2
5
x2
24) y 
3
1
x6
25) y 
4x
x  4x
3
26) y 
 x  2  x  1
Simplify completely and state any restrictions.
27)
x3  125
6 x  24
 2
2
3x  18 x  24 x  25
3a 3b3
29) a  b
4ab
ba
28)
8 x3  27
4x2  6x  9

6 x 2  3x  18
x2
2 x 2  162
2
30) x 2 2 x  63
4 x  8x  4
x 2  49
Be sure to look over your quiz and homework for other types of problems!
x 1