Algebra flashcards, diagrams and study guides

c: they focus on interpersonal relations among the members

d: it deals with treatment of psychotic discorders

d: prevent an array of educational deficits and psychological problems

TRUE: The rows become the columns of AT so this makes sense.

FALSE: The nonzero rows of B form a basis. The first three rows of A may be linear dependent

TRUE by the Rank Theorem. Also since dimension of row space = number of nonzero rows in echelon form = number pivot columns = dimension of column space

An expression that contains numbers, operations, and one or more symbols.

The numerical factor of a term that contains a variable.

A term without a variable.

True

False

True

y = a (x-h)^2 + k

y = ax^2 +bx +c

the highest or lowest point on a parabola; (h, k)

The graph of which of the following basic functions is increasing on the interval (-∞,∞)? A. f(x)=1/x B. f(x)=|x| C. f(x)=x^2 D. f(x)=∛x

Identify the collection of three functions whose graphs are all symmetric about the origin. A. y=1/x, y=x, and y∛x B. y=x^3, y=3, and y=1/x C. y=|x|, y=1/x, and y=x^3 D. y=x^3, y=x^2, and y=√x

Identify the collection of three functions that are all even. A. y=x, y=x^2, and y=y=1/x, y=x, and y=√x B. y=-3, y=x^2, and y=|x| C. y=|x|, y=√x, and y=2 D. y=x^2, y=3, and y=1/x

A number with more than two factors

a group of twelve

A whole number that has exactly two factors, 1 and itself.

Let a and b be integers with b>0. Then there exists unique integers q and r with the property that a=bq+r, where 0<=r<b

A positive integer d such that d is a common divisor of a and b and if d' is any other common divisor of a and b, then d' | d. d = gcd(a,b)

the group of all transformations under which the object is invariant with composition as the group operation.

The span of the vectors of the linear transformation ex: [1,0;0,2;0,1][s;t] = [s;2t;t] = Im(A)

Le U = subspace of R^n. Then, the orthogonal component of U is the set U^ortho = {v in R^n : v*u = 0 for all u in U }

vectors are orthogonal if the dot product between them is zero. there's a symbol for this it looks like perpendicular symbol because it is

Polynomials and rational functions are examples of ___ functions.

Exponential and logarithmic functions are examples of nonalgebraic functions, also called ___ functions.

The exponential function given by e^x is called the ___ ___ function, and the base e is called the ___ base.

Groups 3-12

Group 1

Group 2

Constant

cohesion

Transition

caring confrontation

A process that is used to solve quadratic equations set equal to 0. This process forces a quadratic function to be a perfect square trinomial that can be solved by taking square roots. It is also the process that allows us to derive the equation for the quadratic formula.

a polynomial function of degree n & leading coefficient a,n is a function of a form f(x)=a,n x^n + a,n-1 x^n-1... (a,n cannot = 0) where n is a ------------- & a1 are -------- numbers

a ---------- function is a second-degree polynomial function, & its graph is called a -----------

the graph of a quadratic function is symmetric about its -------

A number multiplied by a variable in an algebraic expression.

A symbol used to represent a quantity that can change

A symbol that indicates the mathematical operation to perform with the operands.

C/Col Jacob A. Caparella

C/Lt Col Mikaela G. Vega

C/Maj Brian Milla