Algebra 2 - Function Characteristics

Study Notes

Function Characteristics Vocabulary

Domain: All possible x-values for a function.
Range: All possible y-values for a function.
x-intercept: The point where the function intersects the x-axis, represented as (x, 0).
y-intercept: The point where the function intersects the y-axis, represented as (0, y).
Function: A relation that pairs each element in the domain with exactly one element in the range, ensuring each x correlates to one y.
One-to-one function: A function in which each element of the range corresponds to exactly one element of the domain; every y has a unique x.
Vertical Line Test: A visual method used to assess if a relation is a function by checking if each x-value corresponds to only one y-value.
Horizontal Line Test: A visual method to determine if a function is one-to-one by checking if each y-value corresponds to only one x-value.
Maximum: The highest point of a graph, visually resembling a peak.
Minimum: The lowest point of a graph, visually resembling a valley.
Vertex: The point on a graph that is either the highest (maximum) or the lowest (minimum) of the function.
Turning Point: A point where the graph's direction changes, marking transitions from increasing to decreasing or vice versa; includes maximums and minimums.
Inflection Point: A point on the graph where the concavity changes between concave up and concave down.
Increasing Interval: An x-interval indicating where the function rises as x increases, represented in the form (x, x).
Decreasing Interval: An x-interval indicating where the function falls as x increases, represented in the form (x, x).
End behavior: Describes the behavior of y-values as x approaches negative or positive infinity, noted as x → -∞, y → and x → ∞, y → .