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Absolute Value Equations and Inequalities Lesson 2.5 Absolute Value Function Whatever you put into the function comes out positive -3 +7 +3 +7 2 Absolute Value Function Definition x if x 0 x abs( x) x if x 0 Use the abs( ) function on your calculator 3 Absolute Value Function Note the graph of y = | x | Table of values 4 Absolute Value Equation Let k be a positive number a x b k means … a x b k or a x b k Then So we just solve two equations Try it 3x 5 35 Solve analytically Solve graphically Absolute Value Inequalities |a x + b | < k is equivalent to -k<ax+b<k - k < a x + b and a x + b < k 3x 5 7 7 6 Absolute Value Inequalities |a x + b | > k is equivalent to a x + b < -k or a x + b > k 3x 5 7 7 ) ) 7 Try It Out! |15 – x | < 7 Solve symbolically |5x – 7 | > 2 Show graphical solution 8 Application Lou Scannon, the human cannon ball plans to travel 180 feet and land squarely on a net with a 70 foot long safe zone. What distances D can Lou travel and still land safely on the net? Use an absolute value inequality to describe the restrictions on D 9 Assignment Lesson 2.5 Page 154 Exercises 1 – 53 EOO 73, 75, 83 10