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6.5 Solving Open Sentences involving Absolute Value Remember the absolute value is the distance from zero on |x – 4| = 5 Write the equation without the absolute values and a number line. then again with the other sign after the =. Absolute value means you are going to have x – 4 = 5 OR x – 4 = -5 2 equations! Solve. The expression inside x = 9 or x = -1 the absolute value Solution is {-1,9} symbols is either positive or negative. Try These Solve |b + 6| = 3 {-9, –3} You may get the answer and be asked for the equation! -4 1 6 Find the middle between the 2 numbers. 1 How many spaces did you move to get there? 5 Plug that information into an equation: |x – middle| = spaces you moved to get there |x – 1| = 5 Try this one Write the equation for this graph. 7 12 17 What is the middle #? 12 How many spaces did you move to get there? 5 Plug it into the equation |x – 12| = 5 Graphing absolute value functions An absolute value function is a function written as f(x) = |x| when f(x) > 0 for all values of x. It’s sometimes known as a piecewise function: a function that can be written using two or more “pieces” or expressions. Think V for Value!!! x if x 0 f ( x) x if x 0 Try This One Graph f(x) = |x – 4| Set x – 4 = 0 x = 4 The V-point is @ (4,0) Slope is 1 to the right of (4,0) (positive) x - 4 Slope is –1 to left of (4,0) (negative) –x + 4 Homework p. 325 1-6. Check them with me before you begin your homework. #42 p. 325 7-35 odd, 47, 49-51