# Week 8 - Room 10.docx.pdf - In-class Worksheet Week...

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In-class Worksheet Week Polynomial and Rational Inequalities (Section 3.6) Names of everyone in this group: Juan Del Barrio, Albert Asante Your breakout room number is: 10 ------------------------------------------------------------------------------------------------------------------------------------------------------- SEGMENT #1 Scribe: Recall that in the pre-class worksheet, you saw how to solve polynomial and rational functions given their graphs. Here we look at another method, which is the algebraic method, for solving these inequalities. A polynomial inequality is any inequality that can be put into one of the forms , f , f 0 f ( x ) < 0 ( x ) > 0 ( x ) ≤ , where is a polynomial function. r f ( x )≥0 o f 1) We want to solve, graph the solution set on a real number line and also write the solution set in interval notation: x 6 x 3 2 + 1 < 5 Step 1: Write the inequality in the form (the solutions of this inequality will be the same as the f ( x ) < 0 solutions of the inequality in the question). 3x^2+16x+5<0 Step 2: Solve the equation . The real solutions are the boundary points. f ( x ) = 0 x= -1/3,-5 The boundary points for are x= -1/3, -5 x 6 x 3 2 + 1 + 5 = 0