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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Section 4.4
Polynomial and Rational Inequalities
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2 22 1 0 by graphing 2Sol 1ve x x f x x x
x
yx-intercepts are 2 with multiplicity 2 (touches) and -1 with multiplicity 1 (crosses). y-intercept is 4.
End behavior is like f(x) = x3.
x
y
Where is this function less than 0?
1 or , 1x x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
x
y
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2 2
2 20 by graphing 4 4Solve .9 9
fx xx 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
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
