Understanding the Absolute Value Function: Explaining How f(x) = |x| Returns the Distance of x from Zero on the Number Line

f(x) = |x|

The function f(x) = |x| is an absolute value function

The function f(x) = |x| is an absolute value function. It takes any real number x as input and returns the absolute value of x.

The absolute value of a number is its distance from zero on the number line. So, if x is positive or zero, the absolute value of x is equal to x. If x is negative, the absolute value of x is equal to -x.

For example, let’s evaluate f(x) for some different values of x:

1. When x = 3:
f(3) = |3| = 3 (because 3 is positive)

2. When x = -5:
f(-5) = |-5| = 5 (because -5 is negative, so we take its positive value)

3. When x = 0:
f(0) = |0| = 0 (because 0 is neither positive nor negative)

Graphically, the absolute value function f(x) = |x| can be represented as a symmetric V-shaped graph. The V opens up from the point (0, 0) on the coordinate plane.

To summarize, the function f(x) = |x| returns the absolute value of x, which is the distance of x from zero on the number line.

More Answers: