Instructor’s Solutions Manual For Calculus, Volume 1 by OpenStax Gilbert Strang All Chapters 1-6

OpenStax Calculus Volume 1 Instructor Answer and Solution Guide




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 y x y
–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. Yes, a function

2.
x y x y
–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. Yes, a function

3.
x y x y
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 y x y
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. Yes, a function

,OpenStax Calculus Volume 1 Instructor Answer and Solution Guide


5.
x y x y
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. Yes, a function

6.
x y x y
–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 they exist, then simplify.
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   4 x 2  3x  1
Answer: a. 1 b. 2 c. 28 d. 4 x 2  3x  1 e. 4a 2  3a  1 f. 4a 2  8ah  4h 2  3a  3h  1

2
9. f  x 
x
2 2 2 2
Answer: a. Undefined b. 2 c d.  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. 6 x  5 e. 6a  5 f. 6a  6h  5

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

x
14. f  x 
x  16 2

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

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

3
16. h  x 
x 4
2

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

17. f  x   1  x  2
Answer: x  2; y  1; x  1; y  1  2

1
18. f  x 
x 9
Answer: x  9; y  0; no intercepts

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

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

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