## f(x) = |x|

### The function f(x) = |x| represents the absolute value of x

The function f(x) = |x| represents the absolute value of x. The absolute value of a number is defined as the distance of that number from zero on a number line.

For positive values of x, the absolute value function simply returns the value of x itself. So if x is positive, f(x) equals x.

For negative values of x, the absolute value function returns the negation of x, or the positive value of x. So if x is negative, f(x) equals -x.

Essentially, the absolute value function “strips away” any negativity from x, giving you the positive value of x.

To illustrate this, let’s consider a few examples:

1. If x = 4, then f(x) = |4| = 4, since 4 is already positive.

2. If x = -5, then f(x) = |-5| = 5, since the absolute value function flips the sign to positive.

3. If x = 0, then f(x) = |0| = 0, since the distance of 0 from zero is 0 itself.

The graph of the absolute value function is a V-shaped symmetrical graph, opening upwards or downwards depending on whether the leading coefficient is positive or negative.

Remember, the absolute value function only deals with magnitudes and disregards the original sign of the number.

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