In "Algebra Functions," a **function** is described as a set of data that has one distinct output (y) for each input (x). A function also describes the relationship between inputs (x) and outputs (y). As a testament to the various patterns between x and y, several types of functions exist.

### Algebraic Functions

- Linear
- Absolute Value
- Quadratic
- Exponential
- Trigonometric
- Rational
- Logarithmic

Each type of Algebraic function is its own family and possesses unique traits.

If you want to understand the characteristics of each family, study its **parent function**, a template of domain and range that extends to other members of the family. This article focuses on the linear parent function.

### Linear Parent Function Characteristics

- The equation of the linear parent function is
*y*=*x.* - Refer to Linear Parent Function for the graph of
*y*=*x.* - Domain: All real numbers
- Range: All real numbers
- The slope, or rate of change, is constant.

### Linear Function Flips, Shifts, and Other Tricks

Family members have common and contrasting attributes. If your dad has a big nose, then you probably have one as well. Nonetheless, just as you are different from your parents, so is a subsequent function different from its parent.

**Note**: *Any changes to the equation will alter the graph.*

**Vertical Shifts***y* = *x*+1

The graph shifts up 1 unit.

*y*= *x*-4

The graph shifts down 4 units.

**Changes in Steepness***y*= 3*x*

The graph becomes steeper.

*y* = ½*x*

The graph becomes flatter.

**Negative Influence***y*=

The graph flips and slopes downward, instead of upward. (See Calculate a Negative Slope.)