MATH-1340 HANDOUT 2 (Lesson 2)
1. If f ( x)   x 2  x  4 , find f ( 2), f (0), and f (4).
2. If f ( x)   x 3  x 2  3 , find f ( 3), f (0), and f (2).
3. If f ( x) 
x  4  3x , find f (4), f (8), and f (13).
x
4. If f ( x) 
, find f ( 2), f (0), and f (3).
x 3
Exercises 5-8: If a and h are real numbers, find:
(a) f (a )
(b) f ( a )
(c)  f (a )
(d) f (a  h)
f (a  h)  f (a)
(e) f (a)  f (h)
(f)
, provided h  0
h
5. f ( x)  5 x  2
6. f ( x)  3  4 x
7. f ( x)  x 2  x  3
8. f ( x)  2 x 2  3x  7
Exercise 9-12: If a is a positive real number, find:
1
1
(a) g  
(b)
(c) g ( a )
g (a)
a
9. g ( x)  4 x 2
10. g ( x)  2 x  5
11. g ( x) 
2x
2
x 1
12. g ( x) 
Exercise 13-20: Find the domain of f .
13. f ( x)  2 x  7
14.
15.
f ( x) 
17.
f ( x) 
19.
f ( x) 
9  x2
x 1
x  4x
3
2x  3
x 2  5x  4
(d)
g (a)
x2
x 1
f ( x)  8  3 x
16.
f ( x) 
18.
f ( x) 
20.
f ( x) 
x 2  25
4x
6 x  13x  5
2
4x  3
x2  4
31.
An open box is to be made from a rectangular piece of cardboard having dimensions 20 inches 
30 inches by cutting out identical squares of area x 2 from each corner and turning up the sides.
Express the volume V of the box as a function of x.
32.
An aquarium of height 1.5 feet is to have a volume of 6 ft3. Let x denote the length of the base,
and let y denote the width.
(a)
Express y as a function of x.
(b)
Express the total number of square feet of glass needed as a function of x.
35.
A hot-air balloon is released at 1:00 P.M. and rises vertically at a rate of 2 meters per second.
An observation point is situated 100 meters from a point on the ground directly below the
balloon. If t denotes the time (in seconds) after 1:00 P.M., express the distance d between the
balloon and the observation point as a function of t.
Answers:
1.  6,  4,  24
5c.  5a  2
3.  12,  22,  36
5d. 5a  5h  2
7a. a 2  a  3
11a.
4
a2
9b.
2a
2
a 1
13.

19.
 , 4  (4 , )
7
2
, 
11b.
1
4a 2
a2  1
2a
15. [ 3, 3]
3
2
35. d  2 t 2  2500
5b.  5a  2
5e. 5a  5h  4
7e. a 2  h 2  a  h  6
9c. 4a
11c.
5f. 5
7c.  a 2  a  3
7b. a 2  a  3
7d. a 2  2ah  h 2  a  h  3
9a.
5a. 5a  2
2 a
a 1
7f. 2a  h  1
9d. 2a
11d.
2a 3  2a
a2  1
17. All real numbers except  2, 0, and 2
31. V  4 x 3  100 x 2  600 x