Parent Functions

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.

Vertical shifts:

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.)