Algebra 2 Parent Functions Quiz & Flashcards

Study Notes

Parent Functions

Linear Parent Function: A foundational function characterized by a constant rate of change, represented graphically as a straight line.
Absolute Value Parent Function: Produces a V-shaped graph, reflecting the magnitude of a number without regard to its sign.
Quadratic Parent Function: Forms a parabolic curve, demonstrating the relationship between variables squared.

Parent Function Equations

Linear Parent Equation: Defined as f(x) = x, its graph is a straight line through the origin with a slope of 1.
Absolute Value Equation: Expressed as f(x) = |x|, with a vertex at the origin and a U-shaped graph.
Quadratic Equation: Expressed as f(x) = x², producing a parabola that opens upward.
Constant Equation: Defined as f(x) = 1, producing a horizontal line at y = 1.

Transformations

Reflection: Changes the orientation of the graph by flipping it across the x-axis or y-axis.
Vertical Translation: Adjusts the graph's position vertically, moving it up or down along the y-axis.
Horizontal Translation: Alters the position of the graph horizontally, moving it left or right along the x-axis.
Vertical Stretch: Occurs when a function is multiplied by a factor greater than one, resulting in a steeper graph.
Vertical Shrink: Happens when a multiplying factor lies between 0 and 1, making the graph flatter.

Function Shifts

+/- a number inside the function: Affects the graph's horizontal position, shifting it left or right based on the value added or subtracted.
+/- a number outside the function: Influences the graph's vertical position, shifting it up or down depending on whether the value is positive or negative.

Description

This quiz focuses on key parent functions and their transformations, ideal for Algebra 2 students. You'll explore definitions and equations for linear, absolute value, and quadratic parent functions. Test your knowledge and enhance your understanding of this foundational concept in algebra.