1-6 Absolute Value and Distance Goal Recognize the connections between absolute value and distance, and the implications the definition of absolute value.

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Presentation transcript:

1-6 Absolute Value and Distance Goal Recognize the connections between absolute value and distance, and the implications the definition of absolute value has for distinguishing x from |x|. Big Idea The absolute value of a # and the distance between 2 #s on a # line are closely related.

The _____________________ on a number line is: | x - x | 2 1 distance between 2 points The ___________ of a _______ its ___________. absolute valuenumber is distance from 0

1. Evaluate the following. a. | - ⅝ | ⅝ b. | | | - 76 | 76 c. |3 · 10 ³| |.003| Solve a. | x | = 1212 x = b. | m | = -8 No solution x = An absolute value cannot equal a negative number

3. Find the distance between the points with coordinates -4 and | |= | -189 |= 4. Solve | x-8 | = 25. Graph the solutions on a number line. x-8 = x = 33 andx-8 = x = -17        ··

5. Graph the expression | x-1 | on a coordinate grid. Use a graphing calculator or by hand with a table of values. For the calculator when entering the expression, it must read abs(x-1). To insert the absolute value, click 2 nd, then catalog (which is above the prgm key). Scroll down and select abs( then click enter and finish typing.