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

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Identify the x-intercept(s) and vertical asymptote(s) of the graph of the function.

1. y 5 x2 1 2x 2 15

} x2 2 36

2. y 5 x2 2 2x 1 1

} x2 2 2

3. y 5 2x 2 1

} x2 1 7

Graph the function.

4. f (x) 5 2x 1 4

} x2 2 16

5. f (x) 5 2x2

} x2 1 5x 1 4

6. f (x) 5 x2 2 3 }}

2x2 1 5x 2 12

x

y

2

2

x

y

2

2

x

y

2

2

7. f (x) 5 x2 2 25

} x 2 4

8. f (x) 5 5x2 1 7x 1 2

} 2x2 2 8

9. f (x) 5 2x2 1 3

} x3

x

y

4

4

x

y

2

2

x

y

2

2

10. Critical Thinking Give an example of a rational function whose graph has two vertical asymptotes, x 5 6 and x 5 0, and does not have any x-intercepts.

In Exercises 11 and 12, use the following information.

Pollution Suppose organic waste was dumped into a pond. Part of the decomposition process includes oxidation, whereby oxygen that is dissolved in the pond water is combined with decomposing material. The oxygen level L in the pond can be modeled

by L 5 t2 2 t 1 1

} t2 1 1

where t represents the number of weeks after the waste is

dumped. The normal oxygen level in the pond is L 5 1.

11. Graph the model for 0 ≤ t ≤ 20.

t

L

4 8 12 16 20

0.20.40.60.81.0

00

Oxy

gen

leve

l

Time (weeks)

12. Explain how the oxygen level changed during the 20 weeks after the waste was dumped.

Practice BFor use with the lesson “Graph General Rational Functions”

Les

so

n 5

.3

Algebra 2Chapter Resource Book5-30

Lesson

5.3

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Lesson Graph General Rational Functions, continuedPractice Level B

1. x-intercepts: 25, 3; vertical asymptotes: x 5 26, x 5 6 2. x-intercept: 1; vertical asymptotes: x 5 2 Ï

}

2 , x 5 Ï}

2

3. x-intercept: 1 }

2 ; vertical asymptote: none

4.

x

y

2

−2

5.

x

y

2−2

6.

x

y

2

4

7.

x

y

8

8

8.

x

y

4

4

9.

x

y

2

2

10. Sample answer: y 5 3 }

x2 2 6x

11.

t

L

4 8 12 16 20

0.20.40.60.81.0

00

Oxy

gen

leve

l

Time (weeks)

12. The oxygen level dropped to 50% of normal and then slowly increased to 95% of normal.

Practice Level C

1. x-intercept: none; vertical asymptotes: x 5 2 Ï

}

2 , x 5 Ï}

2 2. x-intercept: 21; vertical

asymptote: none 3. x-intercepts: 1 }

2 , 3; vertical

asymptotes: x 5 2 1 } 2 , x 5

1 }

2

4.

x

y

2

2

5.

x

y

2

2

6.

x

y

4

22

7.

x

y

2

22

8.

x

y

2

4

9.

x

y

4

4

10. Sample answer: y 5 2x2 1 2x

} x2 2 5x 1 6

11. h 5 320

} πr2 12. S 5 2πr2 1

640 } r

13.

0 1 2 3 4 5 6 r 0

150200250300350400450

S

Radius (cm)

Su

rfac

e A

rea

(cm

2 )

7 8 9

14. r 5 3.7 cm, h 5 7.4 cm

Study Guide

1.

x

y

1

1

2.

x

y

5

3

3.

x

y

1

3

4.

x

y

4

4

5. 8 cm by 8 cm by 8 cm

Algebra 2Chapter Resource BookA6

5.3