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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