comparisons and operations
Inequality between a linear and a quadratic function
This is a graphic representation of
an inequality
f(x) > g(x), in which:
f(x) is a linear function.
g(x) is a quadratic function; its graph intersects the x-axis at
(-1,0) and (3,0) and the y axis at (0,-6).
The solutions of the inequality are:  .
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Construct correspondence rules for functions f(x) and g(x).
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Leave g(x) as is and change f(x) to another
linear function to obtain modified inequalities f(x) > g(x) with
the following properties (if you think it cannot be done, explain why):
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All solutions of the inequality are positive.
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1.
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The inequality has no solutions.
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2.
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All numbers are solutions of the inequality.
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3.
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The solutions of the new inequality are the same
as those of the original one.
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4.
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The solutions of the inequality are: -2< x < -1
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5.
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The solutions of the inequality are: -1 < x < 3
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6.
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The solutions of the inequality are: x>1 or
x<-1
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7.
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Leave f(x) as is and change g(x) to a different
quadratic function to obtain modified inequalities f(x)>g(x) with the
properties listed in 1-7 above (if you think it cannot be done, explain why).
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