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The absolute value function of a real number returns its value irrespective of its sign, whereas the sign (or signum) function returns a number's sign irrespective of its value. The following equations show the relationship between these two functions:
To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero.
Learn what absolute value means, how to write it with bars or abs function, and how to use it in algebra and arithmetic. See examples of absolute value of positive, negative and zero numbers, and how to subtract with absolute value.
Learn what absolute value is, how to evaluate expressions with absolute value, and how to graph absolute value functions. See the definition, properties, and examples of absolute value for real numbers and complex numbers.
Learn how to think about absolute value as distance from zero, and practice finding absolute values. See examples, problems, tips, and comments on absolute value symbol and real-life scenarios.
This topic covers: Solving absolute value equations. Graphing absolute value functions. Solving absolute value inequalities.
Absolute value equations are equations involving expressions with the absolute value functions. This wiki intends to demonstrate and discuss problem solving techniques that let us solve such equations. A very basic example would be as follows: Find all values of x x satisfying |x-2| + |x-4| = 4. ∣x −2∣+ ∣x− 4∣ = 4.
