Each type of algebra 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. The most basic parent function is the linear parent function.

## Algebra Function Basics

In the phrase "algebra functions," a function** **is 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:

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

## Linear Parent Function Characteristics

In algebra, a linear equation is one that contains two variables and can be plotted on a graph as a straight line. Key common points of linear parent functions include the fact that the:

- Equation is y = x
- Domain and range are real numbers
- Slope, or rate of change, is constant.

You can see the physical representation of a linear parent function on a graph of y = x.* *

## Linear Function Flips, Shifts, and Other Tricks

Family members have common and contrasting attributes. If your dad has a big nose, for example, 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.

For the linear parent functions below, note that any changes to the equation will alter the graph.

y = x+1

The graph shifts up 1 unit.

y=x-4

The graph shifts down 4 units.

**Changes in steepness:**

y= 3x

The graph becomes steeper.

y = ½x

The graph becomes flatter.

**Negative influence:**

y =

The graph flips and slopes downward, instead of upward. (This is also called a negative slope.)