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=Function
s=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
Answer:=a.=Domain=== 0,1,2,3,= range=== −3,=−2,=−1,0,1,2,3=b.=No,=not=a=function=4.
0 0
x y x y
1 1 5 1
2 1 6 1
3 1 7 1
Answer:=a.=Domain=== 1,=2,3,=4,5,6,7,=range=== 1=b.=Yes,=a=function
4 1
,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 ) = 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
=2
=1 =1= = x =+ =2 = a =− =2 = a=+=h=−=2=
Answer:=a. −= = b. −= c. =1 d. =−= = f.
7 =
6 7=−=3x e. 3a=+=7 3a=+=3h=+=7
10
, 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=functi
ons.
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
Complete Chapter Solutions Manual are
= = = =
included (Ch 1 to 6)
= = = = =
,OpenStax=Calculus=Volume=1 Instructor=Answer=and=Solution=Guide
Chapter=1=Function
s=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
Answer:=a.=Domain=== 0,1,2,3,= range=== −3,=−2,=−1,0,1,2,3=b.=No,=not=a=function=4.
0 0
x y x y
1 1 5 1
2 1 6 1
3 1 7 1
Answer:=a.=Domain=== 1,=2,3,=4,5,6,7,=range=== 1=b.=Yes,=a=function
4 1
,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 ) = 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
=2
=1 =1= = x =+ =2 = a =− =2 = a=+=h=−=2=
Answer:=a. −= = b. −= c. =1 d. =−= = f.
7 =
6 7=−=3x e. 3a=+=7 3a=+=3h=+=7
10
, 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=functi
ons.
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
