Chapter 1 y4
Graphs, Functions, and Models
y4 y4 y4
Toy 4 graphy 4 (−1,y44)y 4 wey 4 movey 4 fromy 4 they 4
4 1y 4 unity 4 toy 4 the
Checky4 Youry4 Understandingy4 Sectiony4 1.1 lefty 4 ofy 4 they 4 y-
axis.y 4 y 4 Theny 4 wey 4 movey 4 4y 4 unitsy 4 upy 4 f
1. They4pointy4
—(y 4 5,y40)y4isy4ony4any4axis,y4soy4ity4isy4no the
ty4iny4anyy4quadrant.y4They4statementy4isy4false. x-axis.
Toy4graphy4(0,y42)y4wey4doy4noty4movey4toy4they4
2. They4orderedy4pairy4 —(1,y 4 6)y4isy4locatedy41y4unity4righ
4ory4they4lefty4ofy 4 they4y-
ty4ofy4they4originy4andy46y4unitsy4below—y4it.y4They4orde
axisy4sincey4they4firsty4coordinatey4isy40.y 4 Fromy4
redy4pairy4(y 4 6,y41)y4isy4locatedy46y4unitsy4lefty4ofy4— the
originy 4 wey4movey42y4unitsy4up.
y4origin
— y4and y41 y4 unity4above y4it. y 4 Thus, y4(1, y 4 6) y 4 a
ndy 4 (y 4 6,y41)y 4 doy 4 noty 4 namey 4 they 4 samey 4 point.y Toy4graphy4(2,—y 4 2)y4wey4movey4fromy4they4origin
4 They 4 statementy4isy4false. unitsy4toy4they4righty 4 ofy 4 they 4 y-
y
axis.y 4 Theny 4 wey 4 movey 4 2y 4 unitsy 4 downy 4 from
3. True;y4they4firsty4coordinatey4ofy4ay4pointy4isy4alsoy4call y4x-axis.
( 1,y
edy4they4abscissa. 44)y 4 4
4. True;y 4 they 4 pointy 4 (y 4 2y 4 7)y 4 isy 4 2y 4 unitsy 4 lefty 4 ofy 4 they 4 originy 4 and
−y 4 , 2y 4 (0,y42)
(
7y4unitsy4abovey4it.y 4
2 y40)(2,y 4
4,
43y4unitsy4toyy44the 2) y4lefty 4 ofy 4 they 4 y-
5. True;y4they4secondy4coordinatey4ofy4ay4pointy4isy4alsoy4 (
axis. y
3,y 4
4 Then y 4 we y 4 movey 4 5y 4 unitsy 4 downy 4 fr
y 4 5)
calledy4they4ordinate. hey4x-axis.
6. False;y 4 they 4 pointy 4 (0,y4−3)y 4 isy 4 ony 4 they 4 y-axis.
Exercisey 4 Sety 4 1.1
1. Pointy 4 Ay 4 isy 4 locatedy 4 5y 4 unitsy 4 toy 4 they 4 lefty 4 of
y 4 they 4 y-axisy 4 andy 4 4y 4 unitsy 4 upy 4 fromy 4 they 4 x-
axis,y 4 soy 4 itsy 4 coordinatesy 4 arey 4 (−5,y44).
Pointy 4 By 4 isy 4 locatedy 4 2y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-axisy 4 andy42y4unitsy4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(2,y4−2).
Pointy4Cy4isy4locatedy40y4unitsy4toy4they4righty4ory4le
fty4ofy4they4y-
axisy4andy45y4unitsy4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(0,y4−5).
Pointy 4 Dy 4 isy 4 locatedy 4 3y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-axisy 4 andy45y4unitsy4upy4fromy4they 4 x-
axis,y4soy4itsy4coordinatesy4arey4(3,y45).
Pointy 4 Ey 4 isy 4 locatedy 4 5y 4 unitsy 4 toy 4 they 4 lefty 4
ofy 4 they 4 y-axisy 4 and
4y 4 unitsy 4 downy 4 fromy 4 they 4 x-
axis,y 4 soy 4 itsy 4 coordinatesy 4 arey 4 (−5,y4−4).
Pointy 4 Fy 4 isy 4 locatedy 4 3y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-
axisy 4 andy40y4unitsy4upy4ory4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(3,y40).
3.y 4 Toy4graphy4(4,y40)y4wey4movey4fromy4they4originy44y4
unitsy4toy4they4righty4ofy4they4y-
axis.y 4 Sincey4they4secondy4coordinatey4isy40,y4wey4doy4
noty4movey4upy4ory4downy4fromy4they4x-axis.
Toy4graphy4
−(yy44 3,y 4 5)y4wey4movey4fromy4they4originy
y4−
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
,5.y 4 Toy 4 graphy 4 (y 4 5,y41)y 4 wey 4 movey 4 fromy 4 they 4 orig
iny 4 5y 4 unitsy 4 toy 4 they4lefty4 ofy4 they4 y-
axis.y 4 Theny4 wey4 movey4 1y4 unity4 upy4 fromy4 they4 x- —
axis.
Toy4graphy4(5,y41)y4wey4movey4fromy4they4originy45y4uni
tsy4toy4they4righty4ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 1y 4 unity 4 upy 4 fromy 4 they
4 x-axis.
Toy4graphy4(2,y43)y4wey4movey4fromy4they4originy42y4uni
tsy4toy4they4righty4ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 3y 4 unitsy 4 upy 4 fromy 4 they
4 x-axis.
Toy4graphy4(2,y 4 1)y4wey4movey4fromy4they4originy42y4u —
nitsy4toy4they4righty 4 ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 1y 4 unity 4 downy 4 fromy 4 they
4x-axis.
Toy4graphy4(0,y41)y4wey4doy4noty4movey4toy4they4righty4
ory4they4lefty4ofy 4 they4y-
axisy4sincey4they4firsty4coordinatey4isy40.y 4 Fromy4they4o
riginy 4 wey4movey41y4unity4up.
y
7.y4They4firsty4coordinatey4representsy4they4yeary4andy4the
y4corre- 4
(2,y43)
y4spondingy4secondy4coordinatey4representsy4they4numbe 2
ry4ofy4citiesy4servedy4byy4Southwesty4Airlines.y 4 They4or ( (0,y41)
5,y41) (5,y4
deredy4pairsy4arey 4 (1971,y 4 3),y 4 (1981,y 4 15),y 4 (1991,y
4 2 2y 4 (2,y
4 32),y 4 (2001,y 4 59),y 4 (2011,y 4 72), 4 y 4 1)
andy4(2021,y4121). 4
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
,
, 14 Chaptery 4 1:y 4 y 4 Graphs,y 4 Functions,y
dy 4 Models
9.y 4 Toy 4 determiney 4 whethery 4 (−1,y4−9)y 4 isy 4 ay 4 solut 2ay4+y45by4 = y43y4
ion,y 4 substitute 3
−1y4fory4xy4andy4−9 2y4·y40y4+y45y4·y 4 ?y 4 3y4
5y 4
y4fory4y.y4yy4
=y47xy4−y42
−9y 4 ?¯ 7(−1)y4− 0y4+y4¯ 3y4
¯ y42 3y 4 ¯ y43y 4 TRUE
−7y4−y42 ³ 3y4´ y4
−9y 4 ¯ y4−9 TRUE They4equationy43y4=y43y4isy4true,y4soy4 0,y4 isy4ay4so
They 4 equationy 4 −9y 4 =y 4 −9y 4 isy 4 true,y 4 soy 4 (−1,y4−9 5
)y 4 isy 4 ay 4 solution.y4Toy4determiney4 whethery4 (0,y42)y 15. Toy 4 determiney 4 whethery 4 (−0.75,y42.75)y 4 isy 4 ay
ion,y 4 substi-y4tutey4−0.75y4fory4xy4andy42.75y4fo
4 isy4 ay4 solution,y4 substitutey4 0y4 for
xy4andy42y4fory4y. x2y4−y4y2y 4 = y43y4
yy 4 =y 4 7xy4−y42
2y 4 ?y 4 7y4· (−0.75)2y4−y4(2.75)2y 4 ?¯ y43y4
y40y4−y42
¯ 0— 2 0.5625y4−y47.5625
¯
2 ¯ y4−2 FALSE −7y 4 ¯ y43y 4 FALSE
They4equationy4 2y4=y4−2y4 isy4 false,y4 soy4 (0,y42)y4 isy4 They 4 equation− −
noty4 ay4 solution. 7y 4 =y 4 3y 4 isy 4 false,y 4 soy 4 (y 4
³ y42y4 3y4´ y4 2.75)y 4 isy 4 noty 4 ay4solution.
11.y 4 Toy4 determiney4 whethery4 ,y4 isy4 ay4solution,y4 s Toy 4 determiney 4 whethery 4 (2,y4−1)y 4 isy 4 ay 4 solu
2 4 substitutey 4 2
ubstitutey 4
3y 4 4 3
3y 4 fory4xy4andy4−1y4fory4y.
fory4 xy4andy 4 fory4 y.
4 x2y4−y4y2y 4 = y43y4
6xy4−y44yy 4
22y4−y4(−1)2y 4 ?¯ y43y4
2= y41y43 —
4 1
6y4·y 4 −y44y4· ¯
y4 3?y4
y 4 1y4
4y 4 3y 4 ¯ y43y 4 TRUE
4
¯ 3y
4
— They 4 equationy 4 3y4 =y4 3y 4 isy 4 true,y 4 soy 4 (2,y4−1)
1 ¯ y41y 4 TRU ay 4 solution.
E ³ y42y 4 3y4
They4 equationy4 1y4=y41y4 is , 17.y4 Graphy45xy4−y43yy4=y4−15.
´ 3y4
y4 true,y4 so y 4 isy 4 ay 4 solut
To
x y 4 findy 4 they 4 x-
³ y4
3y4´ y44 ion.
Toy4determiney4whethery4 1,y4 isy4ay4solution,y4substitutey41y4for intercepty 4 wey 4 replacey 4 yy 4 withy 4 0y 4 andy 4 solve
2 5xy4−. y43y4·y40 y4=y 4 −15
3
xy4andy 4 fory4y. 5xy 4 =y 4 −15
2y 4
6xy4−y44yy 4 = y41y4 xy4 =y4 −3
They 4 x-intercepty 4 isy 4 (−3,y40).
3y 4
6y4·y41y4−y44y4·y 4 ?y Toy 4 findy 4 they 4 y-
2
4 1y4 intercepty 4 wey 4 replacey 4 xy 4 withy 4 0y 4 andy 4 solve
y.
6y4−y46¯
5 y4·y40y4−y43yy4 =y4−15
0y 4 ¯ y41y 4 FAL ³ y 4 3y4
SE ´ −3yy 4 =y4 −15
They 4 equationy 4 0y4=y41y 4 isy 4 false,y 4 soy 4 y 4 1,y4 yy 4 = y45y4
2
isy 4 noty 4 ay 4 solutio They 4 y-intercepty 4 isy 4 (0,y45).
n.
³ y4 1y4 Wey 4 ploty 4 they 4 interceptsy 4 andy 4 drawy 4 they
4y4´ y4 4 thaty 4 contains
13.y 4 Toy4determiney4whethery4 −y4 ,y4−y4 isy4ay4solutio
2 5
1 4
n,y4substitute
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
Graphs, Functions, and Models
y4 y4 y4
Toy 4 graphy 4 (−1,y44)y 4 wey 4 movey 4 fromy 4 they 4
4 1y 4 unity 4 toy 4 the
Checky4 Youry4 Understandingy4 Sectiony4 1.1 lefty 4 ofy 4 they 4 y-
axis.y 4 y 4 Theny 4 wey 4 movey 4 4y 4 unitsy 4 upy 4 f
1. They4pointy4
—(y 4 5,y40)y4isy4ony4any4axis,y4soy4ity4isy4no the
ty4iny4anyy4quadrant.y4They4statementy4isy4false. x-axis.
Toy4graphy4(0,y42)y4wey4doy4noty4movey4toy4they4
2. They4orderedy4pairy4 —(1,y 4 6)y4isy4locatedy41y4unity4righ
4ory4they4lefty4ofy 4 they4y-
ty4ofy4they4originy4andy46y4unitsy4below—y4it.y4They4orde
axisy4sincey4they4firsty4coordinatey4isy40.y 4 Fromy4
redy4pairy4(y 4 6,y41)y4isy4locatedy46y4unitsy4lefty4ofy4— the
originy 4 wey4movey42y4unitsy4up.
y4origin
— y4and y41 y4 unity4above y4it. y 4 Thus, y4(1, y 4 6) y 4 a
ndy 4 (y 4 6,y41)y 4 doy 4 noty 4 namey 4 they 4 samey 4 point.y Toy4graphy4(2,—y 4 2)y4wey4movey4fromy4they4origin
4 They 4 statementy4isy4false. unitsy4toy4they4righty 4 ofy 4 they 4 y-
y
axis.y 4 Theny 4 wey 4 movey 4 2y 4 unitsy 4 downy 4 from
3. True;y4they4firsty4coordinatey4ofy4ay4pointy4isy4alsoy4call y4x-axis.
( 1,y
edy4they4abscissa. 44)y 4 4
4. True;y 4 they 4 pointy 4 (y 4 2y 4 7)y 4 isy 4 2y 4 unitsy 4 lefty 4 ofy 4 they 4 originy 4 and
−y 4 , 2y 4 (0,y42)
(
7y4unitsy4abovey4it.y 4
2 y40)(2,y 4
4,
43y4unitsy4toyy44the 2) y4lefty 4 ofy 4 they 4 y-
5. True;y4they4secondy4coordinatey4ofy4ay4pointy4isy4alsoy4 (
axis. y
3,y 4
4 Then y 4 we y 4 movey 4 5y 4 unitsy 4 downy 4 fr
y 4 5)
calledy4they4ordinate. hey4x-axis.
6. False;y 4 they 4 pointy 4 (0,y4−3)y 4 isy 4 ony 4 they 4 y-axis.
Exercisey 4 Sety 4 1.1
1. Pointy 4 Ay 4 isy 4 locatedy 4 5y 4 unitsy 4 toy 4 they 4 lefty 4 of
y 4 they 4 y-axisy 4 andy 4 4y 4 unitsy 4 upy 4 fromy 4 they 4 x-
axis,y 4 soy 4 itsy 4 coordinatesy 4 arey 4 (−5,y44).
Pointy 4 By 4 isy 4 locatedy 4 2y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-axisy 4 andy42y4unitsy4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(2,y4−2).
Pointy4Cy4isy4locatedy40y4unitsy4toy4they4righty4ory4le
fty4ofy4they4y-
axisy4andy45y4unitsy4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(0,y4−5).
Pointy 4 Dy 4 isy 4 locatedy 4 3y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-axisy 4 andy45y4unitsy4upy4fromy4they 4 x-
axis,y4soy4itsy4coordinatesy4arey4(3,y45).
Pointy 4 Ey 4 isy 4 locatedy 4 5y 4 unitsy 4 toy 4 they 4 lefty 4
ofy 4 they 4 y-axisy 4 and
4y 4 unitsy 4 downy 4 fromy 4 they 4 x-
axis,y 4 soy 4 itsy 4 coordinatesy 4 arey 4 (−5,y4−4).
Pointy 4 Fy 4 isy 4 locatedy 4 3y 4 unitsy 4 toy 4 they 4 righty 4
ofy 4 they 4 y-
axisy 4 andy40y4unitsy4upy4ory4downy4fromy4they4x-
axis,y4soy4itsy4coordinatesy4arey4(3,y40).
3.y 4 Toy4graphy4(4,y40)y4wey4movey4fromy4they4originy44y4
unitsy4toy4they4righty4ofy4they4y-
axis.y 4 Sincey4they4secondy4coordinatey4isy40,y4wey4doy4
noty4movey4upy4ory4downy4fromy4they4x-axis.
Toy4graphy4
−(yy44 3,y 4 5)y4wey4movey4fromy4they4originy
y4−
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
,5.y 4 Toy 4 graphy 4 (y 4 5,y41)y 4 wey 4 movey 4 fromy 4 they 4 orig
iny 4 5y 4 unitsy 4 toy 4 they4lefty4 ofy4 they4 y-
axis.y 4 Theny4 wey4 movey4 1y4 unity4 upy4 fromy4 they4 x- —
axis.
Toy4graphy4(5,y41)y4wey4movey4fromy4they4originy45y4uni
tsy4toy4they4righty4ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 1y 4 unity 4 upy 4 fromy 4 they
4 x-axis.
Toy4graphy4(2,y43)y4wey4movey4fromy4they4originy42y4uni
tsy4toy4they4righty4ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 3y 4 unitsy 4 upy 4 fromy 4 they
4 x-axis.
Toy4graphy4(2,y 4 1)y4wey4movey4fromy4they4originy42y4u —
nitsy4toy4they4righty 4 ofy 4 they 4 y-
axis.y 4 Theny 4 wey 4 movey 4 1y 4 unity 4 downy 4 fromy 4 they
4x-axis.
Toy4graphy4(0,y41)y4wey4doy4noty4movey4toy4they4righty4
ory4they4lefty4ofy 4 they4y-
axisy4sincey4they4firsty4coordinatey4isy40.y 4 Fromy4they4o
riginy 4 wey4movey41y4unity4up.
y
7.y4They4firsty4coordinatey4representsy4they4yeary4andy4the
y4corre- 4
(2,y43)
y4spondingy4secondy4coordinatey4representsy4they4numbe 2
ry4ofy4citiesy4servedy4byy4Southwesty4Airlines.y 4 They4or ( (0,y41)
5,y41) (5,y4
deredy4pairsy4arey 4 (1971,y 4 3),y 4 (1981,y 4 15),y 4 (1991,y
4 2 2y 4 (2,y
4 32),y 4 (2001,y 4 59),y 4 (2011,y 4 72), 4 y 4 1)
andy4(2021,y4121). 4
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
,
, 14 Chaptery 4 1:y 4 y 4 Graphs,y 4 Functions,y
dy 4 Models
9.y 4 Toy 4 determiney 4 whethery 4 (−1,y4−9)y 4 isy 4 ay 4 solut 2ay4+y45by4 = y43y4
ion,y 4 substitute 3
−1y4fory4xy4andy4−9 2y4·y40y4+y45y4·y 4 ?y 4 3y4
5y 4
y4fory4y.y4yy4
=y47xy4−y42
−9y 4 ?¯ 7(−1)y4− 0y4+y4¯ 3y4
¯ y42 3y 4 ¯ y43y 4 TRUE
−7y4−y42 ³ 3y4´ y4
−9y 4 ¯ y4−9 TRUE They4equationy43y4=y43y4isy4true,y4soy4 0,y4 isy4ay4so
They 4 equationy 4 −9y 4 =y 4 −9y 4 isy 4 true,y 4 soy 4 (−1,y4−9 5
)y 4 isy 4 ay 4 solution.y4Toy4determiney4 whethery4 (0,y42)y 15. Toy 4 determiney 4 whethery 4 (−0.75,y42.75)y 4 isy 4 ay
ion,y 4 substi-y4tutey4−0.75y4fory4xy4andy42.75y4fo
4 isy4 ay4 solution,y4 substitutey4 0y4 for
xy4andy42y4fory4y. x2y4−y4y2y 4 = y43y4
yy 4 =y 4 7xy4−y42
2y 4 ?y 4 7y4· (−0.75)2y4−y4(2.75)2y 4 ?¯ y43y4
y40y4−y42
¯ 0— 2 0.5625y4−y47.5625
¯
2 ¯ y4−2 FALSE −7y 4 ¯ y43y 4 FALSE
They4equationy4 2y4=y4−2y4 isy4 false,y4 soy4 (0,y42)y4 isy4 They 4 equation− −
noty4 ay4 solution. 7y 4 =y 4 3y 4 isy 4 false,y 4 soy 4 (y 4
³ y42y4 3y4´ y4 2.75)y 4 isy 4 noty 4 ay4solution.
11.y 4 Toy4 determiney4 whethery4 ,y4 isy4 ay4solution,y4 s Toy 4 determiney 4 whethery 4 (2,y4−1)y 4 isy 4 ay 4 solu
2 4 substitutey 4 2
ubstitutey 4
3y 4 4 3
3y 4 fory4xy4andy4−1y4fory4y.
fory4 xy4andy 4 fory4 y.
4 x2y4−y4y2y 4 = y43y4
6xy4−y44yy 4
22y4−y4(−1)2y 4 ?¯ y43y4
2= y41y43 —
4 1
6y4·y 4 −y44y4· ¯
y4 3?y4
y 4 1y4
4y 4 3y 4 ¯ y43y 4 TRUE
4
¯ 3y
4
— They 4 equationy 4 3y4 =y4 3y 4 isy 4 true,y 4 soy 4 (2,y4−1)
1 ¯ y41y 4 TRU ay 4 solution.
E ³ y42y 4 3y4
They4 equationy4 1y4=y41y4 is , 17.y4 Graphy45xy4−y43yy4=y4−15.
´ 3y4
y4 true,y4 so y 4 isy 4 ay 4 solut
To
x y 4 findy 4 they 4 x-
³ y4
3y4´ y44 ion.
Toy4determiney4whethery4 1,y4 isy4ay4solution,y4substitutey41y4for intercepty 4 wey 4 replacey 4 yy 4 withy 4 0y 4 andy 4 solve
2 5xy4−. y43y4·y40 y4=y 4 −15
3
xy4andy 4 fory4y. 5xy 4 =y 4 −15
2y 4
6xy4−y44yy 4 = y41y4 xy4 =y4 −3
They 4 x-intercepty 4 isy 4 (−3,y40).
3y 4
6y4·y41y4−y44y4·y 4 ?y Toy 4 findy 4 they 4 y-
2
4 1y4 intercepty 4 wey 4 replacey 4 xy 4 withy 4 0y 4 andy 4 solve
y.
6y4−y46¯
5 y4·y40y4−y43yy4 =y4−15
0y 4 ¯ y41y 4 FAL ³ y 4 3y4
SE ´ −3yy 4 =y4 −15
They 4 equationy 4 0y4=y41y 4 isy 4 false,y 4 soy 4 y 4 1,y4 yy 4 = y45y4
2
isy 4 noty 4 ay 4 solutio They 4 y-intercepty 4 isy 4 (0,y45).
n.
³ y4 1y4 Wey 4 ploty 4 they 4 interceptsy 4 andy 4 drawy 4 they
4y4´ y4 4 thaty 4 contains
13.y 4 Toy4determiney4whethery4 −y4 ,y4−y4 isy4ay4solutio
2 5
1 4
n,y4substitute
cy 4 2025y4Pearsony4Educati
Copyrighty4◯
