Vocab Flashcards
Increasing Interval
f(x) increases there is an increase in the x value
Decreasing Interval
f(x) decreased in the x value
Turning Point
function changes from increasing to decreasing or decreasing to increasing
Zero
value of x for which f(x) equals 0 (y=0) (x,0)
Maximum or Absolute Max
highest point
Minimum or Absolute Min
lowest point
Average Rate of Change
the average rate at which one quantity is changing with respect to something else changing (ex. y2-y1/x2-x1)
Relative Maximum
high point(s) second highest point
Relative Minimum
low point(s) second lowest point
Transformation
a change in position, size, or shape
Parameters
a constant in a function rule that can be changed (such as a or b in y =ax+b)
Even Function
f(-x)=f(x) its reflection across the y-axis are identical
Odd Function
f(-x)=f(x) the graph is the same when it is reflected across the y-axis as it is when reflected across the x-axis
Horizontal Stretch
g(x) if the constant is between 0 and 1 it will be a horizontal stretch
Horizontal Compression
if the constant is greater than 1 we will get a horizontal compression (ex. 1/3 would be 3)
Vertical Stretch
if the constant is greater than 1 we will get a stretch
Vertical Compression
if the constant is between 0 and 1 it will be a compression
End Behavior
the trends in the y-value of a function as the x-values increase or decrease without bound
Even Function
a function in which f(-x) =f(x) for all x in the domain of the function
Function
A relation in which every domain value is paired with exactly one range value
Parent Function
an equation in the simplest form of a family of functions
Absolute Function
f(x) would be equal to the absolute value { } f(x)=a lx-hl =k
Piece-wise-defined Function
a piecewise function is a function whose domain is partitioned into several intervals on which the function may be defined differently. Piecewise definition is actually a way of specifying the function, rather than a characteristic of the resulting function itself
Quadratic Function
In mathematics, a quadratic function of a single variable is a function of the form where is its variable, and , , and are coefficients. The expression , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
Exponential Function
The exponential function is a mathematical function denoted by or. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Vertex
(h,k)
AOS (Axis of Symmetry)
The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part.
Linear Function
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
