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# Parent Functions

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
• 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= 3x
The graph becomes steeper.

y = ½x
The graph becomes flatter.

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

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