Understanding the Function f(x) = |x|: Behavior, Graph, and Summary

f(x)=|x|

The given function is f(x) = |x|

The given function is f(x) = |x|. In this function, the absolute value function is denoted by |x|. The absolute value of a number x is defined as the distance between x and 0 on the number line.

To understand the behavior of the function, let’s evaluate it for different values of x:

When x is positive (x > 0), the absolute value of x is simply x. So, for x > 0, f(x) = x.

When x is negative (x < 0), the absolute value of x is -x (since the distance between x and 0 is the same as the distance between -x and 0). So, for x < 0, f(x) = -x. For x = 0, the absolute value of 0 is 0 since it is equidistant from 0 and -0. Therefore, f(0) = 0. Graphically, the function f(x) = |x| represents a V-shaped graph centered at the origin (0,0). It starts at the origin (0,0) and extends in both the positive and negative directions. The function is symmetric with respect to the y-axis. To summarize: - For x > 0, f(x) = x
– For x < 0, f(x) = -x - For x = 0, f(x) = 0 I hope this clarifies the behavior and graph of the function f(x) = |x|. Let me know if you have any further questions or need additional explanation!

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