lesson practice a 5.2 for use with the lesson “graph
TRANSCRIPT
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Find the vertical asymptote of the graph of the function.
1. f (x) 5 x } x 1 4 2. f (x) 5
7 }
x 2 2 2 3 3. f (x) 5
x 2 6 }
x 1 6
Find the horizontal asymptote of the graph of the function. State the domain and range.
4. f (x) 5 x 2 2
} 2x 1 1 5. f (x) 5 5 }
x 2 1 1 3 6. f (x) 5
6 }
x 2 4
Match the function with its graph.
7. f (x) 5 x 2 2
} x 1 3 8. f (x) 5 x 1 2
} x 2 3 9. f (x) 5 4 }
2x 2 1
A.
x
y
2
2
B.
x
y
2
2
C.
x
y
2
2
Graph the function.
10. f (x) 5 x 2 2
} x 11. f (x) 5
3 } x 1 2 12. f (x) 5
4 }
x 2 1 1 2
x
y
2
2
x
y
2
2
x
y
2
2
In Exercises 13–15, use the following information.
Sports Banquet You are organizing your high school’s sports banquet.
x
A
20 30 40 50 60 70
2030
010
40506070
Number of peoplein attendance
Ave
rage
co
stp
er p
erso
n
0 10
The banquet hall rental is $350. In addition to this one time charge, the meal will cost $8.50 per plate. Let x represent the number of people who attend.
13. Write an equation that represents the total cost C.
14. Write an equation that represents the average cost A per person.
15. Graph the model in Exercise 14.
Practice AFor use with the lesson “Graph Simple Rational Functions”
Les
so
n 5
.2
Algebra 2Chapter Resource Book5-16
Lesson
5.2
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Lesson Model Inverse and Joint Variation, continued 7. k varies jointly with b and the square of c and inversely with d and with the square root of m.
b 5 1 }
a p dk Ï
}
m }
c2 ; b varies jointly with d, k, and with
the square root of m and inversely with the square
of c. c 5 1 }
Ï}
a p
Ï}
dk 4
Î}
m }
Ï}
b ; c varies jointly with
the square roots of d and k and with the
fourth root of m, and inversely with the square root
of b. d 5 a p bc2 }
k Ï}
m ; d varies jointly with b and
the square of c, and inversely with the square root
of m and with k. m 5 a2 p b2c4 }
d2k2 ; m varies jointly
with the square of b and the fourth power of c, and inversely with the square of d and with the square of k.
8. f varies jointly with the cube of g and the square root of h, and inversely with j, k, and the square
of l. g 5 1 }
3 Ï}
a p
3 Ï}
f jk p l2/3
} 6 Ï}
h ; g varies jointly with the
cube roots of f, j, and k, and with the two-thirds power of l, and inversely with the sixth root of h.
h 5 1 }
a2 p f 2j2k2l4
} g6 ; h varies jointly with the square
of f, the square of j, the square of k, and the fourth power of l, and inversely with the sixth power of g.
j 5 a p g3 Ï
}
h }
f kl2 ; j varies jointly with the cube of g
and the square root of h, and inversely with f, k,
and with the square of l. k 5 a p g3 Ï
}
h } f jl2
; k varies
jointly with the cube of g and the square root of h, and inversely with f, j, and with the square of l.
l 5 Ï}
a p Ï}
g3 p 4
Î}
h }
Ï}
fjk ; l varies jointly with the
square root of the cube of g and with the fourth root of h, and inversely with the square roots of f, j, and k.
9. Answers will vary. Sample answer: p 5 114
} t ;
22.8%
10. Answers will vary. Sample answer:
P 5 116
} A
; the person weighs 116 pounds.
Lesson Graph Simple Rational FunctionsTeaching Guide
1. x 5 0; y 5 0; It lies further from the axes but has same asymptotes.
2. The graph is shifted 1 unit to the right and 2 units up from the parent graph.
3. The graph is shifted 3 units to the left and 1 unit down from the parent graph.
Practice Level A
1. x 5 24 2. x 5 2 3. x 5 26
4. y 5 1 }
2 ; domain: all real numbers except 2
1 } 2 ;
range: all real numbers except 1 }
2 5. y 5 3;
domain: all real numbers except 1; range: all real numbers except 3 6. y 5 24; domain: all real numbers except 0; range: all real numbers except 24 7. C 8. A 9. B
10.
x
y
2
2
11.
x
y
−22
12.
x
y
4
2
13. C 5 8.5x 1 350 14. A 5 8.5x 1 350
} x
an
sw
er
s
Algebra 2Chapter Resource BookA2
5.1
5.2
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Lesson Graph Simple Rational Functions, continued15.
x
A
20 30 40 50 60 70
2030
010
40506070
Number of peoplein attendance
Ave
rage
co
stp
er p
erso
n
0 10
Practice Level B
1. x 5 2; y 5 1 2. x 5 4 } 3 ; y 5
2 }
3
3. x 5 3 }
2 ; y 5
1 }
2 4. x 5 2
3 } 2 ; y 5 2
5. x 5 2; y 5 2 6. x 5 22; y 5 2
7.
x
y
2
2
; domain; all real numbers except 23; range: all real numbers except 0
8.
x
y
2
2
; domain; all real numbers except 3; range: all real numbers except 1
9.
x
y
4
2
; domain: all real numbers
except 1 }
2 ; range: all real
numbers except 2
10.
x
y
2
24
; domain: all real numbers except 22; range: all real numbers except 0
11.
x
y
222
; domain: all real numbers
except 2 1 } 2 ; range: all
real numbers except 3 }
2
12.
x
y
2
2
; domain: all real numbers
except 2 }
3 ; range: all real
numbers except 21
13. C 5 32x 1 65 14. A 5 32x 1 65
} x
15.
0 5 10 15 20 25 30 x 0
25303540455055C
Number of months
Tota
l Co
st
16. 52 months
Practice Level C
1. x 5 1; y 5 5 2. x 5 22; y 5 23
3. x 5 1 }
2 ; y 5
3 }
2 4. x 5 2
1 } 4 ; y 5 2
5. x 5 2; y 5 21 6. x 5 2 2 } 3 ; y 5 5
7.
x
y
4
2
; domain: all real numbers except 4; range: all real numbers except 3
8.
x
y
2
2
; domain: all real numbers except 0; range: all real numbers except 22
9.
x
y
2
2
; domain: all real numbers
except 2 } 5 ; range: all real
numbers except 4
10.
x
y
2122
; domain: all real numbers except 21; range:
all real numbers except 2 3 } 2
Algebra 2Chapter Resource Book A3
5.2