Section 4.4 polynomial and rational inequalities

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Section 4.4
Polynomial and Rational
Inequalities

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( ) ( ) ( ) ( ) ( )
2 2
2 1 0 by graphing 2Sol 1ve x x f x x x− + < = − +
−3 −2 −1 1 2 3 4 5 6
−4
−3
−2
−1
1
2
3
4
x
y
x-intercepts are 2 with multiplicity 2
(touches) and -1 with multiplicity 1
(crosses).
y-intercept is 4.
End behavior is like f(x) = x3
.
−3 −2 −1 1 2 3 4 5 6
−4
−3
−2
−1
1
2
3
4
x
y
Where is this function less than 0?
{ } ( )1 or , 1x x < − −∞ −

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7. −5 −4 −3 −2 −1 1 2 3 4 5 6 7
−5
−4
−3
−2
−1
1
2
3
4
5
6
x
y
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( )
2 2
2 2
0 by graphing
4 4
Solve .
9 9
f
x x
x x
x
−
=
−
≥
− −
-intercepts are -2 and 2.
4
-intercept is .
9
x
y
Vertical asymptotes at 3 and 3x x= − =
Horizontal asymptote at 1y =
Where is this function greater
than or equal to 0?
{ }
( ) [ ] ( )
3 or 2 2 or 3
, 3 2,2 3,
x x x x< − − ≤ ≤ >
−∞ − ∪ − ∪ ∞

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