6.5 Solving Open Sentences involving Absolute Value Remember the absolute value is the distance from zero on a number line. Absolute value means you are going to have 2 equations! The expression inside the absolute value symbols is either positive or negative. |x – 4| = 5 Write the equation without the absolute values and then again with the other sign after the =. x – 4 = 5 OR x – 4 = -5 Solve. x = 9 or x = -1 Solution is {-1,9}

Try These Solve |b + 6| = 3 {-9, –3} You may get the answer and be asked for the equation! 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 1 6 -4

Try this one Write the equation for this graph. What is the middle #? 12 How many spaces did you move to get there? 5 Plug it into the equation |x – 12| = 5 17 7 12

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!!!

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