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200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial nequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute Value Inequalities Interval Notation 100 200 300 Applying Inequalitie 100 200 300

200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

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Page 1: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

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Polynomial Inequalities

RationalInequalities

Systems of

Inequalities

DescribingGraphs

Absolute Value

Inequalities

Interval Notation

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ApplyingInequalities

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200

300

Page 2: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve x2<-x+6

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-3<x<2

Page 4: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve x2 + 2 ≥ 3x

Page 5: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x ≤ 1 or x ≥ 2

Page 6: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve x3<x

Page 7: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x < -1 or 0 < x < 1

Page 8: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve

0)2()1(

xx

Page 9: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x < -2 or x > 1

Page 10: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

What is a rational function?

Page 11: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

A function of the form

where and are polynomials.

Page 12: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve

0)3()9( 2

xx

Page 13: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x<-3 or -3<x<3or

x<3 and x≠-3

Page 14: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

y ≥ -x + 1y ≥ -x + 1

y ≥ xy ≥ x

Page 15: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute
Page 16: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

2x - y ≤ 22x - y ≤ 2

2y + x < 22y + x < 2

Page 17: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute
Page 18: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Graph the solution to the Graph the solution to the system of inequalities:system of inequalities:

y ≥ xy ≥ x22 – 2 – 2

x ≥ -3y + 6x ≥ -3y + 6

Page 19: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute
Page 20: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Describe the following Describe the following graph with an inequality.graph with an inequality.

Page 21: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

y≤-x+10

Page 22: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Describe the following graph Describe the following graph with a system of inequalities.with a system of inequalities.

Page 23: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

⅓x – 3 ≤ y ≤ ⅓x + 3

Page 24: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Describe the following graph with Describe the following graph with a system of inequalitiesa system of inequalities..

Page 25: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

0 ≤ y ≤ 2x

x < 3

Page 26: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve | 2x + 3 | < 6

Page 27: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

-4.5 < x < 1.5

Page 28: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve | 5x | > 15

Page 29: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x < -3 or x > 3

Page 30: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve | x + 12 | + 3 > 17

Page 31: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

X < -26 or x > 2

Page 32: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Graph [-9, -5) U (0, ∞) Graph [-9, -5) U (0, ∞) on a number line on a number line

Page 33: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute
Page 34: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve Solve (x + 4)(x – 2)(x - 7)(x + 4)(x – 2)(x - 7) > 0. > 0.

Write the solution in Write the solution in interval notation. interval notation.

Page 35: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

(-4, 2)U(7, ∞)

Page 36: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Solve xSolve x3 3 > 2x. Write the > 2x. Write the solution in interval solution in interval

notation. notation.

Page 37: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

(- ,0) U ( ,∞)(- ,0) U ( ,∞)2 2

Page 38: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

The profit a company earns as a function of items sold, x, is

represented by P(x)=x2+2x-8, write an inequality to describe how many

items need to be sold in order for the company to make a profit.

Page 39: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

x > 2

Page 40: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Your new cell phone plan has a monthly access fee of $28.72 with a flat rate of $0.31 per minute.  If you want to keep your monthly bill under $40, how many minutes per month can you talk on your new cell

phone?

Page 41: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

Let x = number of minutes spent talking

$28.72 + .31x < 40.31x < 11.28

x < 36.38709677 You can use up to 36 minutes per month.

Page 42: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

The height of a rocket in feet is represented by the equation h(t)=-16t2+64t+72, where

t=time, in seconds. For what values of t will the rocket

remain at or above 100 feet from the ground.

Page 43: 200 300 100 200 300 100 200 300 100 200 300 100 200 300 100 Polynomial Inequalities Rational Inequalities Systems of Inequalities Describing Graphs Absolute

0.5 ≤ t ≤ 3.5


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