Honors PreCalculus
Unit 2 Test Review
Name: ___________________________
1. Write the interval notation for the expression “all real numbers between -∞ and 19, inclusive.”
x 2  16
2. Determine all discontinuities of the function f ( x )  3
.
x  64
3. Give the domain of the following functions.
5 x 2  30 x
f ( x) 
10 x
a.
4.
g ( x) 
b.
x 3
( x  6)( x  1)
Solve by factoring.
4 x2  12 x  9
5.
Solve using the quadratic formula.
3x 2  9 x  7  0
6.
x 2  3x  18
f  x  2
x  x  42 , list the domain, range, all
Using the following function,
discontinuities, x and y intercepts.
7.
For the above function, find the limits:
lim f ( x) 
x
lim f ( x) 
x
lim f ( x) 
x6
lim f ( x) 
x7
3x  5
2x  7
8.
Find the x and y intercepts of the function: f ( x) 
9.
For the following function f(x)=x3 + 2x2 - 7x + 3: Using your calculator, determine all local
maximums and minimums. Identify increasing and decreasing intervals.
10.
Write a function that has a horizontal asymptote at y=⅔, an infinite discontinuity at x=4 and
a removable point of discontinuity with an x value of 7.
2  x if x  2

11. h( x)   1
if x  2
 x 2  4 if x  2

12.
11. D:___________
R:___________
C:___________
lim h( x) =
x 2
12. D:___________
R:___________
C:___________
13.
Write f ( x)  2 x  8 as a piecewise function.

 x  3 if x  0
f ( x)   2

 x  2 x if x  0
Find the following limits algebraically
2x  5
14. lim 3
x  x  1
16.
2 x3  5
x  x 3  1
lim
x2  4
18. lim
x 1 x  2
20. xlim

2 x3
x 5
x3  8
15. lim
x 2 x  2
17. lim
x 9
x 3
x 9
1
1
_
x 1 2
19. lim
x 1
x 1