APPC pgs 1-3

slope

Represents the number of unit the line rises or falls for each unit of horizontal change from left to right

point-slope form

𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

slope-intercept form

y=mx+b

general form

Ax+By+C=0

parallel lines

Two distinct nonvertical lines that have the same slope

perpendicular lines

Two nonvertical lines whose slopes are negative reciprocals of each other

function

Relation that assigns each element in set A to exactly one element in set B

domain

The elements of set A (sometimes called x-values or inputs)

range

The elements of set B (sometimes called y-values or outputs)

independent variable

The value that you can choose (sometimes called the domain, x-values, inputs)

dependent variable

The value that you cannot choose (sometimes called the range, y-values, outputs)

function notation

An equation of y in terms of x can be rewritten so that y=f(x).

piecewise-defined function

A function that is defined using two or more expressions for different intervals of the domain

implied domain

In a function with an unspecified domain, the set of all real numbers for which the expression used to define the function is real

Vertical Line Test

A visual test used to determine if a graph represents a function. To be a function the vertical line can only touch graph at most one time

Increasing Function

Describes a function f in which for any two points, a positive change in x results in a positive change in f(x). As x moves to the right the y gets bigger

Decreasing Function

Describes a function f in which for any two points, a positive change in x results in a negative change in f(x). As x moves to the right the y gets smaller

Constant Function

Describes a function f in which for any two points, a positive change in x results in a zero change in f(x)

Maximum

For a function f, the greatest value of f(x). A critical point on the graph of a function where the curve changes from increasing to decreasing

Minimum

For a function f, the least value of f(x). A critical point on the graph of a function where the curve changes from decreasing to increasing

Even Function

A function that is symmetric with respect to the y-axis

Odd Function

A function that is symmetric with respect to the origin

Linear Function

A function of the form 𝑓(𝑥) = 𝐶

Quadratic Function

A function of the form f(x)=ax2 +bx+c, where a is not 0, with parent function f(x)=x^2

Cubic Function

A function of the form f(x)=ax^3 +bx^2 +cx+d, where a is not 0, with parent function f(x)=x^3

Square Root Function

A function that contains a square root of the independent variable, with parent

function f (x) = *square root* x

Absolute Value Function

A function that contains an absolute value of the independent variable, with the parent function of f (x) = |x|

Composite Function

The combining of functions by using the result of one function to evaluate a second function. The composition of function f with function g is defined by [f o g](x)= f[g(x)]

Inverse Function

Two functions f and f^-1 are inverse functions if and only if f[f^-1(x)]=x for every x in the domain of f^-1(x) and f^-1[f(x)]=x for every x in the domain of f(x)

One-To-One

A function in which no x-value is matched with more than one y-value and no y-value is matched with more than one x-value