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10.
[
2
2.7, 6.7] by [
2
6, 6]
A graph of
f
(
x
) is shown. The range of
f
(
x
) is
(
2‘
, 1)
<
[2,
‘
). The values of
c
for which
f
(
x
)
5
c
has
no solution are the values that are excluded from the range.
Therefore,
c
can be any value in [1, 2).
Section 2.3 Exercises
1.
The function
y
5
}
(
x
1
1
2)
2
}
is continuous because it is a
quotient of polynomials, which are continuous. Its only
point of discontinuity occurs where it is undefined. There is
an infinite discontinuity at
x
52
2.
2.
The function
y
5
}
x
2
2
x
1
4
x
1
1
3
}
is continuous because it is a
quotient of polynomials, which are continuous. Its only
points of discontinuity occur where it is undefined, that is,
where the denominator
x
2
2
4
x
1
3
5
(
x
2
1)(
x
2
3) is
zero. There are infinite discontinuities at
x
5
1 and at
x
5
3.
3.
The function
y
5 }
x
2
1
1
1
}
is continuous because it is a
quotient of polynomials, which are continuous.
Furthermore, the domain is all real numbers because the
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 Spring '08
 GERMAN
 Continuity

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