Algebra 2: Key Features of Functions

Key Features of Functions

• Domain: Refers to all possible x-values that a function can take. It represents the left and right boundaries of the graph.
• Range: Represents the set of possible y-values, indicating the minimum and maximum heights of the function.
• Interval Notation: A mathematical notation that expresses a set of real numbers using a pair of values; the left boundary (minimum) and the right boundary (maximum).
• Finding X-Intercepts: To identify x-intercepts, set y equal to zero; the corresponding x-values are where the graph intersects the x-axis.
• Finding Y-Intercepts: To find y-intercepts, set x equal to zero; the resulting y-values are where the graph intersects the y-axis.
• Zero of a Function: The x-value(s) that make the function output zero (f(x) = 0); these values are crucial for understanding where the graph intersects the x-axis.
• X-Intercept: The specific x-coordinate of points where the graph crosses the x-axis.
• Y-Intercept: The specific y-coordinate of points where the graph crosses the y-axis.

Function Behavior

• Maximum: The highest point on the graph, indicating the transition from increasing to decreasing values.
• Minimum: The lowest point on the graph, indicating the transition from decreasing to increasing values.
• Graph and Equation Relationship: Graphs and equations illustrate how variables x and y are interconnected. Changes in x affect y, typically represented as y = f(x), depicting the function's rule of connection.

Additional Key Concepts

• Vertex: The apex or lowest point of a graph, significant in determining the function's overall shape.
• Axis of Symmetry: A line that divides the function into two identical halves, displaying symmetrical properties.
• Reflection: A transformation that flips points across a specified line, creating a mirror image of the original graph.
• Positive Graph: Portions of the graph that lie above the x-axis, indicating positive y-values.
• Negative Graph: Portions of the graph that lie below the x-axis, indicating negative y-values.