Enh. AP Pre calc Unit 1A Vocab

mathematical relation; maps a set of input values to a set of output values (each input has 1 output)

Set of input values

Set of output values

x-values restricted from one value to another (used in graphing) (ex. -4 _< x _< 4)

As one quantity inc., the other inc.

As

ROC is increasing

ROC is decreasing

Use “( )” when doing notation of x-values

The slope of any two points

ROC of a given point (in pre calc: finding ROCs of small intervals near the given point)

Average ROC over any length input value interval is constant (constant ROC) (slope of line)

x-values increasing by the same length amount (ex. x-values are consistently increasing by length 2)

Quadratic functions follow a linear pattern for the average ROC.

Any function representation equal to the formula: p(x) = a_nx^n + a_n-1x^n-1 + a_n-2x^n-2 + … + a_2x^2 + a_1x + a_0 . n =positive integer, a_i = real number for each “i” from 1 to n, a_n = nonzero

The minimums and the maximums of a function

Where it switches from dec. to inc. or at an endpoint if poly. has a restricted domain)

From all of the local extremas, the greatest (max.) or least (mini.) is the absolute extrema.

When a function changes from concave up to concave down (or vise versa). ROC changes from inc. to dec. (vise versa)

a^3-b^3 =(a-b)(a^2+ab+b^2)

a^3+b^3 =(a+b)(a^2-ab+b^2)

Defined as i=(square root) -1 or i^2=-1

Any number written in a+bi form; a and b are real numbers and i is imaginary unit.

i^1=i, i^2=-1, i^3=-i, i^4=1

Two complex numbers in form a+bi and a-bi are called complex conjugates; products of these conjugates are always a real number.

Start w/ factoring then go to…

Case 1: when there is no x-term, solve w square roots

Case 2: coefficient of x^2 term is 1 and coefficient of x term is even number; completing the square

Case 3: equation not factorable, completing square leads to fractions; quadratic formula (x=-b +- (square root) b^2-4ac/2a)

if p(a)=0; if a is real, (x-a) is linear factor of p

Linear factor (x-a) is repeated n times in factored form of polynomial function; corresponding zero has that n amount in multiplicity.

n=1: crosses x-axis

n= odd & greater than or equal to 3: point of inflection (switching roc from incr. to decrease. and vise versa)

n= even: tangent to x-axis

All imaginary roots come in pairs: a+bi and a-bi

A polynomial of degree n has exactly n complex zeros (counting multiplicities)

graph of f(x) is above x-axis

Graph of f(x) is below x-axis

Symmetric over y-axis; f(-x)=f(x); in function, even exponents

Symmetric about the origin; g(-x)=-g(x); odd exponents

Look for when the successive differences become constant.

Describes how a function behaves as it moves indefinitely to the left and right; what happens to y-values as x incr. and decr. w/o bound

Start w right side…

1. If leading coef. is positive, right goes positive

2. If leading coef. is negative, right goes negative

Left:

1. If degree is even; goes same direction as right

2. If degree is odd; goes different than right

1. Graph equation like normal

2. Only keep portion of function indicated by domain restriction

Graph to left of x-value

Graph to the right of the x-value

Segment in between two x-values

Open circle (not included)

Closed circle (included)

Consists of different function rules for diff parts of the domain

1. Absolute value

2. Step (greatest integer)

y= a|x-h| +k, vertex= (h,k)

Steps to graphing:

1. Vertex point

2. a=slope, draw to the right of vertex point

3. Mirror line on left side

Written as f(x)=[|x|] (type of step function)

[|x|]= greatest integer less than or equal to x

1. lim x→a : two sided limit

2. lim x→a+ : right-handed limit

3. lim x→a- : left handed limit

1. Both one side limits must exist

2. Meet at same value