AP PreCalculus Final Exam Review

Function

Inputs related exactly to one output. Use vertical line test.

domain

x - values left and right

Range

y - values up and down

interval

A set of real numbers between two endpoints, often used to describe the domain or range of a function.

Graph increasing

Graph decreasing

Constant graph

Concave up (ROC increasing)

Concave down (ROC decreasing)

point of inflection

x-intercept

y-intercept

Slope

Change in y / x

AROC

average rate of change. Change in y / x

secant line

consecutive equal-length intervals

A method used to approximate the slope of a curve by using a secant line through points that are evenly spaced.

Degree

A unit of measurement for angles, equal to 1/360 of a complete rotation.

Leading coefficient

end behavior

The behavior of a function as the input values approach positive or negative infinity, often described by the limits of the function.

local / relative maximum

local / relative minimum

Global / absolute maximum

global absolute minimum

Extrema

The maximum or minimum values of a function. Absolute (global) extrema and local (relative) extrema.

even degree function

End points both point up or both point down

odd degree function

Graph whose ends points in opposite directions

imaginary number

Product of a real number and the imaginary unit i, defined by its property i²

complex number

Imaginary units expressed in the form a+bi

complex polynomial

conjugate root theorem

if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial.

zero

even function

odd function

limit notation

multiplicities

the degree (exponent) of each factor, or the amount of times a factor appears

Horizontal asymptote

vertical asymptote

Oblique / slant asymptote

rational function

ratio of two polynomial functions where the denominator polynomial is not equal to zero

undefined

the denominator of the expression is equal to zero. Therefore, the expression cannot be determined at that value.

domain restrictions

test points

The test point method can be used to solve quadratic inequalities that have a real number solution. It can also be used for linear inequalities, but it's not the most efficient method.

Hole

binomial theorem

Regression

aims to find a linear relationship to describe the correlation between an independent and possibly dependent variable

residual

the difference between predicted values of y (dependent variable) and observed values of Y

predicted data

used to forecast future outcomes. 

Sequence

an ordered set of numbers, i.e., a set of numbers that “occur one after the other.” For instance, the numbers 2 , 4 , 6 , 8 , … , form a sequence

geometric sequence

Geometric sequences behave like exponential functions, except they are not continuous. Increasing geometric sequences increase by a larger amount each step. (% increase always stays the same!)

Geometric sequence equation

Arithmetic sequence

Arithmetic sequences behave like linear functions, except they are not continuous. Increasing arithmetic sequences increase equally each step. (Slope always stays the same!)

Arithmetic sequence equation

common difference

Constant rate of change in successive terms.

common ratio

Constant proportional change

Exponential growth

growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Exponential decay

decay if it decreases at a rate proportional to its current value

exponent rules

natural base

The natural base, or e, is a fundamental irrational number used in calculus to model exponential growth and decay, and is the base for the natural logarithm

composite function

complex function created by two or more functions

inverse

y = x line

Logarithm

the exponent or power to which a base must be raised to yield a given number

base of a log

Any number greater than 0, but not 1. If base isn’t written it’s understood as a base of 10.

argument of a logarithm

The number that you are taking the logarithm of.

exponential form

A way of writing a number that is multiplied by itself more than once.

logarithmic form

semi-log plot

log properties

Change of base

Natural log

convert log to exponential

Convert exponential to log

Linear equation

Y=mx+b

linear shape

linear asymptotes

A straight line that approaches a curve

linear domain and range

Domain: All real numbers

Range: all real numbers

Absolute value equation

absolute value shape

absolute value asymptote

None

absolute value domain and range

Domain: all real numbers

Range: [0,∞]

quadratic equation

quadratic shape

Quadratic asymptotes

No asymptotes

Quadratic domain and range

Domain: all real numbers

Range: depends if concave down or up… ez tho 😛

square root equation

square root shape

square root asymptotes

No asymptotes

square root domain and range

domain is [0, ∞)

range is [0, ∞)

Cubic equation

Cubic shape

cubic asymptotes

No asymptotes

cubic domain and range

Domain: all real numbers

Range: all real numbers

cube root equation

Cube root shape

cube root asymptotes

No asymptotes

cube root domain and range

Domain: all real numbers

Range: all real numbers

exponential equation

exponential shape

exponential asymptote

Horizontal asymptote

exponential domain and range

Domain: All real numbers

Range: range bounded by the horizontal asymptote