What is absolute value?

Absolute value measures distance from zero, not direction.

Notation:

∣x∣

Examples:

• ∣5∣=5

• ∣−5∣=5

Absolute value is always non-negative.

Absolute value as a piecewise function

Absolute value can be rewritten as:

      {x x≥0

∣x∣=

      {−x x<0​

This means:

• If $x$ is positive, keep it

• If $x$ is negative, flip the sign

Absolute value graphs

• Looks like a V

• Vertex at x=0

• Symmetric about the y-axis

Step Functions

What is a step function?

A step function jumps from one value to another instead of changing smoothly.

It looks like stairs when graphed.

Common example: Greatest Integer Function

f(x)=⌊x⌋

This means:

• Return the largest integer less than or equal to $x$

Examples:

• f(2.7)=2

• f(−1.2)=−2

Important: It does not round.