Download For problems 3 - Garnet Valley School District

Inequalities and Functions Review
Pre-Calc. for AP Prep.
Name: ___________
Date: ___________
Part I: No Calculators
Determine if the following relations are functions.
1)
{(2, 3), (4, 6), (8, 3), (-4, -5)}
2)
x = -2(y + 1)2 + 3
For problems 3 – 8, use the following functions.
2
g ( x )
f ( x) x  3
k ( x)  x 2  2 x  1
x4
3)
(h – f)(½)
4)
k  f x
5)
 f 
  (a)
g
6)
f
h( x)  x3  2 x 2  1
 3

 k 

3


For #7 and 8, if a limited domain is necessary, state the limitations. Then find the
following:
7)
g-1(x)
8)
k-1(x)
In #s 9 – 11, solve each of the inequalities algebraically. Graph the solutions to any
problem for which a number line is provided. In #’s 12 through 18, give the solutions
using interval notation.
9.

2
9 x  4  2 x  5
3
11. 4 x  1  2
13.
4 x3  3x 2  18 x  8  2 x 2  2 x3
10.
1 1
 2  x  2
3 4
12.
x3  2 x 2  3x  0
14.
x2  x  3
0
2 x  1x  52
Graph each inequality or system of inequalities. In #’s 15 -17, give the coordinates of
any corner points that are created.
y  3  2 x  2
2
15.
x 1  3
Part II: Calculators
3 x  5 y  15
17.
y  2x2  x  3
y  4x
16.
8  2x  y
y  x3  4 x 2  x  4
Solve . Give numbers as decimals rounded to the nearest hundredth.
18.
Given P(x) = x 4  2 x 2  3x and Q( x)  6  2 x , give all the values of x for which
P(x) > Q(x).
19.
You are about to take a test that contains questions of type A worth 10 points and
of type B worth 25 points. You must answer at least 3 of type A, but time
restricts answering more than 12. You must answer at least 4 of type B, but time
restricts answering more than 15. In total, you can answer no more than 20
questions. Assuming every question you answer is correct, how many of each
type should you answer to maximize your score? What is your maximum score?