Parent Functions

Math Equation on Blackboard
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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

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= 3x
The graph becomes steeper.

y = ½x
The graph becomes flatter.

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