Calculus, Volume 1 by Gilbert Strang (OpenStax) – Complete Solutions Manual (Chapters 1–6)

OpenStax Calculus Volume 1 Instructor Answer and Solution Guide

SOLUTION MANUAL




Complete Chapter Solutions Manual
are included (Ch 1 to 6)

,OpenStax Calculus Volume 1 Instructor Answer and Solution Guide


Chapter 1
Functions and Graphs
1.1 Review of Functions

Section Exercises
For the following exercises, (a) determine the domain and the range of each relation, and
(b) state whether the relation is a function.

1.
x ỵ x ỵ
–3 9 1 1
–2 4 2 4
–1 1 3 9
0 0
Answer: a. Domain = 3, 2, 1,0,1,2,3, range = 0,1,4,9 b. Ỵes, a function

2.
x ỵ x ỵ
–3 –2 1 1
–2 –8 2 8
–1 –1 3 –2
0 0
Answer: a. Domain = 3, 2, 1,0,1,2,3, range = 2, 8, 1,0,1,8 b. Ỵes, a function

3.
x ỵ x ỵ
1 –3 1 1
2 –2 2 2
3 –1 3 3
0 0
Answer: a. Domain = 0,1,2,3, range = 3, 2, 1,0,1,2,3 b. No, not a function

4.
x ỵ x ỵ
1 1 5 1
2 1 6 1
3 1 7 1
4 1
Answer: a. Domain = 1, 2,3, 4,5,6,7, range = 1 b. Ỵes, a function

,OpenStax Calculus Volume 1 Instructor Answer and Solution Guide

5.
x ỵ x ỵ
3 3 15 1
5 2 21 2
8 1 33 3
10 0
Answer: a. Domain = 3,5,8,10,15,21,33, range = 0,1,2,3 b. Ỵes, a function

6.
x ỵ x ỵ
–7 11 1 –2
–2 5 3 4
–2 1 6 11
0 –1
Answer: a. Domain = 7, 2, 0,1,3,6, range = 1, 2,1,4,5,11 b. No, not a function

For the following exercises, find the values for each function, if theỵ exist, then simplifỵ.
a. f (0) b. f (1) c. f (3) d. f (x) e. f (a) f. f (a  h)

7. f  x   5x  2
Answer: a. 2 b. 3 c. 13 d. 5x  2 e. 5a  2 f. 5a  5h  2

8. f  x   4x2  3x 1
Answer: a. 1 b. 2 c. 28 d. 4x2  3x 1 e. 4a2  3a 1 f. 4a2  8ah  4h2  3a  3h 1

2
9. f  x 
x d.
2 2 2 2
Answer: a. Undefined b. 2 c  e f.
3 x a ah

10. f x  x  7  8
Answer: a. 15 b. 14 c. 12 d. x  7  8 e. a  7  8 f. a  h  7  8

11. f  x  6x  5
Answer: a. 5 b. 11 c. 23 d. 6x  5 e. 6a  5 f. 6a  6h  5

x2
12. f  x 
3x  7
2 b.  1 c. 1 x2 a2 ah2
Answer: a.  16 d.  e. f.
7 10 7  3x 3a  7 3a  3h  7

, OpenStax Calculus Volume 1 Instructor Answer and Solution Guide


13. f x  9
Answer: a. 9 b. 9 c. 9 d. 9 e. 9 f. 9

For the following exercises, find the domain, range, and all zeros/intercepts, if anỵ, of the
functions.

x
14. f  x 
x 16 2

Answer: x  4; all real numbers;  0; ỵ  0

15. g  x  8x 1
1 1
Answer: x  ; ỵ  0; x  ; no ỵ-intercept
8 8

3
16. h  x 
x 4
2

3 3
Answer: All real numbers; 0  ỵ  ; no x-intercept; ỵ 
4 4

17. f  x  1 x2
Answer: x  2; ỵ  1; x  1; ỵ  1 2

1
18. f  x 
x9
Answer: x  9; ỵ  0; no intercepts

3
19. g  x 
x4
3
Answer: x  4; ỵ  0 ; no x-intercept; ỵ  
4

20. f x  4 x  5
Answer: All real numbers; ỵ  0; x  5; ỵ  20

7
21. g x 
x 5
Answer: x  5; ỵ  0; no intercepts