AP Precalculus Unit 1

Function

describes the relationship between variables

Inputs

what goes into the function

Outputs

what comes out of the function

Domain

collection of all inputs

Range

collection of all outputs

Independent Variable

a variable that does not depend on any other variable for its value

Dependent Variable

a variable that depends on another variable for its value

Changes in tandem

Graphical model

Numeric Model

Solution is represented in a table/graph

Analytic model

Verbal model

describes a real-life situation using words as labels and using math symbols to relate the words

Interval

Increasing function

when the value of y increases on increasing the value of x

Decreasing function

the y-value decreases as the x-value increases

Concave up

the rate of change is increasing

Concave down

The rate of change is decreasing

Zeros of a function

Same as x- intercepts, roots, solutions to equations

x-axis

the horizontal axis on a coordinate plane

y-axis

the vertical axis on a coordinate plane

Average rate of change

slope

Constant rate of change

the rate of change in a linear relationship

Positive rate of change

as x increases, y increases

Negative rate of change

As X increases, Y decreases (falling line)

Local (relative) maximum

highest y-value in a certain interval

Local (relative) minimum

lowest y-value in a certain interval

global (absolute) maximum

the highest y-value reached on a graph

global (absolute) minimum

the lowest y-value reached on a graph

Even degree function

a function with a degree of 2, 4, 6, etc. (such as y=x^4)

Odd degree function

a function with a degree of 1, 3, 5, etc. (such as y=x^3)

Points of Inflection

Where concavity changes from up or down or vice versa

vertical translation

An up or down slide; the y-coordinate changes.

horizontal translation

A slide to the right or left; the x-coordinate changes.

multiplicative transformation

vertical dilation

horizontal dilation

reflection

A transformation that "flips" a figure over a mirror or reflection line.

linear regression

a statistical method used to fit a linear model to a given data set

quadratic regression

A statistical method used to fit a quadratic model to a given data set.

Limit Notation

composite function

identify function

inverse function

a function that "undoes" what the original function does

linear function

A function whose graph is a straight line.

quadratic function

A function in which the greatest power of the variable is 2.

Polynomial function

a continuous function that can be described by a polynomial equation in one variable

discrete function

a function of points that are not connected

continuous function

a function that can be graphed with a line or a smooth curve