ap-precal midterm

Input-Output

Relationship between independent (input) values and dependent (output) values

Average Rate of Change

Ratio of change in output values to change in input values over an interval

Concave Up

Average change over equal-length input intervals increases for all small intervals

Concave Down

Average change over equal-length input intervals decreases for all small intervals

Polynomial Functions

Functions with many terms, nonconstant

Increasing

Function rises from left to right

Decreasing

Function falls from left to right

Change in Rate of Change

Change in the ratio of output values to input values over an interval

Secant Line

Line connecting two points to find rate of change

Point of Inflection

Where function changes concavity

Degree

Largest exponent of a polynomial function

Leading Coefficient

Number in front of the variable with the largest exponent

Even/Odd

Symmetry properties of functions

End Behavior

Behavior of a polynomial function at extreme x-values

Limit

Behavior of a function as input values approach a certain value

Conjugate

Pairs of imaginary roots

Multiplicity

Degree of a zero

Tangent

Graph bounces off the x-axis

Transformation

Changes in a function's graph

Dilations

Enlarge or compress the graph vertically or horizontally

Translations

Rigid movements of a graph

Extrema

Maximum and minimum points

Rational Functions

Ratio of two polynomials

Asymptotes

Lines that a graph approaches but never touches

Holes

Missing points in a graph

Polynomial Long Division

Method to rewrite rational functions

Regression

Using data to model a function

Pascal's Triangle

Tool to expand functions

Zeros

Points where the graph intersects the x-axis

Real and Non-Real Zeros

Input values where the output is zero, including imaginary values