Algebra II Vocab

Domain

All possible X values ( If arrow then Domain is Infinity ) LOOK AT VERTICAL LINES

Range

All possible Y Values (if arrow

Constraint

Condition which a solution MUST satisfy. Only SOME Numbers are reasonable, constraint funtions are often modeled by DISCRETE FUNCTINOS (or broken functions)

Continuous Function

Unbroken line or curve

When writing Interval notation, NO “U” WILL BE USED “( , )”

Discrete Function

Discontinuous Function which points are NOT connected

When writing Interval Notation, “U” WILL BE USED

Algebraic Notation

Uses Algebraic expressions. EX: x<2

NO PARENTHESIS

Set-Builder Notation

Uses “{ , }” Braces for indication of a SET.

Similar writing to Algebraic Notation, also uses the “such that”. ex {x | x < }

Interval Notation

sets described as USING ENDPOINTS with either PARENTHESIS OR BRACKETS.

Parenthesis “( , )” means the endpoint is not included in the interval

Bracket’s “[ , ]” mean the endpoint is included in the interval

X intercept

X-coordinate(s) at which the graph crosses the X-axis

Y intercept

Y-coordinate(s) at which the graph crosses the Y-axis

Even Functions

Functions with line symmetry with RESPECT TO THE Y-AXIS

______ functions will “Fold Perfectly” over the y-axis, x values are opposite, y values are the same

f(-x) = f(x)

Odd functions

Functions with POINT SYMMETRY with RESPECT TO THE ORIGIN

______ functions MUST pass through the origin. Opposite s gives opposite y. IN EQUATIONS NO CONSTANTS INCLUDED

f(-x) =-f(x).

Abs. Maximum

HIGHEST POINT on the graph of a function (Y VALUE)

If highest point is an ARROW, NO MAX

Abs. Minimum

LOWEST POINT on the graph of a function (Y VALUE)

If lowest point is an ARROW, NO MIN

Relative Min

Y VALUE, at a “VALLEY” when the function changes from DEC → INC

Relative Max

Y VALUE, at a “PEAK” when the function changes from INC → DEC

Positive Interval

Part of graph ABOVE THE X-AXIS

Look at the x axis values to determine when graph enters the “positive values” (as such any value above 0 is positive)

Negative Interval

Part of graph BELOW THE X-AXIS

Look at the x axis values to determine when graph enters the “negative values” (as such any value below 0 is negative)

End Behavior X values

Behavior of a graph as X APPROCAHES POSITIVE OR NEGATIVE INFINITY

LEFT SIDE of graph: x → -infinity,

RIGHT SIDE of graph x → +infinity

End Behavior Y values

Behavior of a graph as X APPROCAHES POSITIVE OR NEGATIVE INFINITY

UP f(X) approaches POSITIVE INFINITY

DOWN f(X) approaches NEGATIVE INFINITY

Degree

The HIGHEST exponent in and equation ie 2^6. highest exponent is

DEGREE DETERMIENS END BEHAVIOR

If degree is ODD, OPPOSITE END BEHAVIOR,

If degree is EVEN, SAME END BEHAVIOR

Symmetry

Determines whether or not the function is EVEN or ODD, but DOES NOT APPLY TO EXPONENTS, rather the Equation as a whole.

Leading Coeff.

Coefficient of term WITH the highest exponent ie 2^6. Leading coeff is 2

Positive, Odd

As x → - infinity, f(X) → NEGATIVE infinity

As x → +infinity, f(X) → POSITIVE infinity

Positive, Even

As x → - infinity, f(X) → POSITIVE infinity

As x → +infinity, f(X) → POSITIVE infinity

Negative, Odd

As x → - infinity, f(X) → POSITIVE infinity

As x → +infinity, f(X) → NEGATIVE infinity

Negative, Even

As x → - infinity, f(X) → NEGATIVE infinity

As x → +infinity, f(X) → NEGATIVE infinity

Transformation

The MOVEMENT of a function in the coordinate plane

Translation

(Transformation) SLIDES function in the SAME DISTANCE AND DIRECTION

USEING f(x)= a(x-h)+k

Translates up

F(X) + k: k > 0

k refers to the Y VALUE

Translates down

F(X) + k: k < 0

k refers to the Y VALUE

Translates right

F(x - h): h > 0

h refers to the X VALUE

Translates left

F(x - h): h < 0

h refers to the X VALUE

Reflection

Transformation where a figure, line or curve is FLIPPED over a Line of Reflection

Reflection on X-axis

When the PARENT FUNCTION (x + 2) is multiplies by -1, -f(x) is a…

Reflection on Y-axis

When the VARIABLE ONLY (x only!) is multiplied by -1, f(-x) is a…

Dilation

(Transformation) which STRETCHES or COMPRESSES (shrinks) the graph of a function

A value

VERTICLE; stretches and compression

B value

HORIZONTAL; stretches and compressions

VS

af(x), |a| > 1 (a is greater than 1)

“a” represents the constant value (number, no x) BUT given no parenthesis, would be the number attached to x

VC

af(x), 0 < |a| < 1 (a is greater than 0, less than 1)

“a” represents the constant value (number, no x) BUT given no parenthesis, would be the number attached to x