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Polynomial and Rational Inequalities and Interval Notation

Polynomial and Rational Inequalities and Interval Notation. Mrs. King Pre-Calculus. www.highlands.edu/wcotter/Powerpt/Math_ PPT /Sec02_9_Supplement. ppt. Example 1. We can also express this solution with a graph. -2. Notice that the open circle translates into a parenthesis.

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Polynomial and Rational Inequalities and Interval Notation

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  1. Polynomial and Rational Inequalitiesand Interval Notation Mrs. King Pre-Calculus

  2. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Example 1 We can also express this solution with a graph. -2 Notice that the open circle translates into a parenthesis. A third way to express this solution is by using interval notation.

  3. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Example 2 We can express this situation with a graph. -1 5 We can also express this graph with interval notation.

  4. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Example 3 We can express this situation with a graph. -1 5 We can also express this graph with interval notation.

  5. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Exercise 1 Translate the graph into interval notation. -3 5 Solid circles are brackets. Open circles are parenthesis.

  6. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Exercise 2 Translate the graph into interval notation. 3 Arrows translate into infinity signs with parenthesis. Always.

  7. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Exercise 3 Translate the graph into interval notation. Arrows translate into infinity signs with parenthesis. Negative infinity always goes to the left. Positive infinity always goes to the right.

  8. www.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.pptwww.highlands.edu/wcotter/Powerpt/Math_PPT/Sec02_9_Supplement.ppt Exercise 4 Translate the graph into interval notation. -8 10 An open circle is always a parenthesis. Negative infinity always goes to the left. Positive infinity always goes to the right.

  9. Linear Inequalities

  10. Polynomial Inequalities • The graph of y=f(x) lies above the x-axis exactly when f(x)>0 and below the x-axis exactly when f(x)<0.

  11. Practice Problem • Set the inequality “equal” to zero. • Graph on your graphing calculator. • Find the zeros. • Write the answer in interval notation.

  12. Practice Problem

  13. Rational Inequalities • The behavior of a rational function f(x) is determined by the x-intercepts and asymptotes of the function.

  14. Practice Problem

  15. Homework Page 369 #21-24, 29, 30, 35, 41-44, 64, 74

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