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 ah
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
x2
12. f x
3x 7
2 1 1 x2 a2 ah2
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
x4
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
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