Unit 1 - Precalc

VLT (Vertical Line Test)

A method used to determine if a graph represents a function, though it may not always be conclusive.

Rate of Change

The slope of the graph of a function, indicating how the function's values change with respect to its inputs.

Function is positive

Means the function's output is above the x-axis.

Function is increasing

Means the function has a positive slope and is going upward.

Concave Up

A graph that curves upwards, where the rate of change is increasing.

Concave Down

A graph that curves downwards, where the rate of change is decreasing.

Average Rate of Change

Calculated as the difference in function values divided by the difference in input values over a given interval.

Instantaneous Rate of Change

The rate of change at a specific point, approximated by using average rates over small intervals.

Tangent Line

A line that touches a curve at one point, indicating the instantaneous rate of change.

Secant Line

A line that intersects a curve at two or more distinct points, indicating the average rate of change over an interval.

Polynomial Function

A function expressed as a polynomial, characterized by a degree that is a positive integer.

Local Extrema

Points where the function switches between increasing and decreasing, or at endpoints of the interval.

Absolute Extrema

The greatest and least y-values of a function within a given interval.

Point of Inflection

A point where a function changes from concave up to concave down, or vice versa.

Multiplicity of a root

The number of times a particular root appears, affecting how the graph behaves at that root.

Even Functions

Functions that are symmetric about the y-axis; satisfies f(-x) = f(x).

Odd Functions

Functions that are symmetric about the origin; satisfies f(-x) = -f(x).

End Behavior

The behavior of a function as the input values approach positive or negative infinity.

Remainder Theorem

When a polynomial is divided by (x-c), the remainder of the division is equal to f(c).

Factor Theorem

States that if f(c)=0, then (x-c) is a factor of the polynomial f(x).