SOLUTION MANUAL
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 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
2 d. 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
a−2 a+h−2
c. 16 d. − x + 2 e.
2 1 1
Answer: a. − b. − 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
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 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
2 d. 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
a−2 a+h−2
c. 16 d. − x + 2 e.
2 1 1
Answer: a. − b. − 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
