Name ——————————————————————— Date ————————————

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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