Absolute Value Function
The absolute value function is a mathematical function that gives the distance between a number and zero on a number line
The absolute value function is a mathematical function that gives the distance between a number and zero on a number line. The absolute value of a number, denoted by |x|, is always non-negative.
The definition of the absolute value function is as follows:
– For a positive number x, the absolute value is the number itself: |x| = x.
– For a negative number x, the absolute value is the opposite (negation) of the number: |x| = -x.
For example:
– The absolute value of 5 is 5, since 5 is a positive number: |5| = 5.
– The absolute value of -3 is 3, since -3 is a negative number: |-3| = 3.
– The absolute value of 0 is 0, since zero has no distance from itself: |0| = 0.
The absolute value function has various applications in mathematics and real-life scenarios. It is commonly used to express distances, differences, or magnitudes that need to be considered as positive values. It is also useful in solving equations and inequalities involving absolute values.
When graphed on a coordinate plane, the absolute value function typically has a “V” shape. The graph is symmetric with respect to the y-axis and passes through the point (0, 0). The steepness of the graph’s slope changes at the point where x = 0.
In summary, the absolute value function is a function that represents the distance between a number and zero on a number line. It is denoted by |x| and has different definitions depending on whether the number is positive or negative. The function is widely used in mathematics and has a distinctive “V” shape when graphed.
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