Linear Parent Functions (Algebra Help)

Linear Parent Functions (Algebra Help) 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 LinearAbsolute ValueQuadraticExponentialTrigonometricRationalLogarithmic 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 numbersThe 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 Shiftsy x1The graph shifts up 1 unit. y x-4The graph shifts down 4 units. Changes in Steepnessy 3xThe graph becomes steeper. y  ½xThe graph becomes flatter. Negative Influencey  The graph flips and slopes downward, instead of upward. (See Calculate a Negative Slope.)