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Absolute Value Functions!! Day One Should we do this later? No, DO NOW Complete the Absolute Value Exploration Sheet with a Pal Hot News! After School Help w/Mr. Meyer in the Media Center Every Wednesday 2:15-3:00 PM Tuesdays and Thursdays by Appointment (Send me an email or ask me the day before) tmeyer2@eden.rutgers.edu http://honorsalgebra2meyer.wikispaces.com/ That’s an Aardvark! f(x)=|x| Reflect Part of y=x f(x)=a*|x| f(x)=|x-h| f(x)=|x|+k Rules for Graphing Absolute Value Functions The graph of f(x)=a*|x-h|+k has the following characteristics: A) Vertex (h,k), symmetric with x=h B) V-shaped, opens UP if a>0 and DOWN if a<0 C) Wider than parent function if |a|<1 and narrower than parent function if |a|>1 Graph These Absolute Value Functions Graphing! 1) Find the vertex. (1,1) 2) “a” is negative, and so, it opens downwards. 3) Find one other point on the graph. (Use the slope.) (2,0) 4) Use symmetry to plot the point on the other side of the vertex. Writing Equations 1) Identify the vertex. (3,1) 2) Identify the a value. Point (4,3) is on the graph. 3=a*|4-3|+1. a=2 3) Substitute into y=a*|x-h|+k. y=2*|x-3|+1 Write it Piecewise! Write the absolute value equation as a piecewise function. 1) So if x £ 3 , the equation of the line is found as follows: a-Slope is -2 from the graph c-The point (2,3) is on the line. Use this to find the intercept: f(x)=-2x+b 3=-2*(2)+b, b=7. So if x £ 3, the line has equation f(x)=-2x+7 Write it Piecewise 2) So if x>3, the equation of the line is found in the same way to be f(x)=2x-5. 3) Write it together as a piecewise as: { f(x)= -2x+7; (-∞, 3] 2x-5; (3, ∞) Practice Hit “Y=“ Enter into Y1 a function of the form f(x)=a*|x-h|+k To get absolute value, hit ‘MATH’, scroll right to ‘NUM’, and hit 1:abs( For this exercise, pick a, h, and k (your parameters) between -5 and 5. Hit ‘GRAPH’ Trade calculators with your partner and try to come up with the absolute value and piecewise equations for your partners graph. Graphing Calculators On your graphing calculators, graph f(x)= . (Hit “Y=“, Enter “ “ after Y1, Be Sure to Close the Parentheses, Hit “GRAPH”) What do you see?