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Function

Domain

x²x³

x²/x³

Assigns to each number in its domain another number... Takes 1…

Consists of all numbers for which the rule makes sense. All n…

x²⁺³

x²⁻³

Function

Assigns to each number in its domain another number... Takes 1…

Domain

Consists of all numbers for which the rule makes sense. All n…

Difference Quotient

Piecewise functions

Logarithmic Function

Trigonometric Functions

Function expressed by two or more different formulas over dif…

and/or A^y = X

Sine X ... Cos X ... Tan X ... Sec X ... CSC X ... CoTan X

Difference Quotient

Piecewise functions

Function expressed by two or more different formulas over dif…

Metacognition ( Five things to remembe…

Five Step Problem Solving process (alg…

Function

Write Equations of Parallel and Perpen…

1. Assess the task—Get a handle on what is involved in comple…

1. Familiarize yourself with the problem... 2. Identify the kno…

a function from a set X to a set Y is a rule for assigning to…

Metacognition ( Five things to remembe…

1. Assess the task—Get a handle on what is involved in comple…

Five Step Problem Solving process (alg…

1. Familiarize yourself with the problem... 2. Identify the kno…

End behavior

Exponential Decay

Exponential Growth

Limit

The appearance of a graph as it is followed farther and farth…

A model for decay of a quantity for which the rate of decay i…

This model is used for such phenomena as inflation or populat…

The value that a function or expression approaches as the dom…

End behavior

The appearance of a graph as it is followed farther and farth…

Exponential Decay

A model for decay of a quantity for which the rate of decay i…

Limit Does NOT Exist when:

Formal Definition of Limit:

Squeeze Theorem

Continuous at point x=c

1. f(x) approaches different number from L and R... 2. Vertical…

if a fuc is between two other functions, both having a limit…

Limit Does NOT Exist when:

1. f(x) approaches different number from L and R... 2. Vertical…

Formal Definition of Limit:

Completing statements with meaning of…

Completing statements with meaning of…

If f(x) is continuous at x = r then li…

The expression that defines the deriva…

"we can keep the numbers produced by f(x)=____ as close as we…

"we can keep the numbers produced by (whatever is beside limi…

f(r)

Completing statements with meaning of…

"we can keep the numbers produced by f(x)=____ as close as we…

Completing statements with meaning of…

"we can keep the numbers produced by (whatever is beside limi…

Non Differentiable functions

Derivative

Integration

Fractional Exponents

undefined slope or vertical tangent line.

Slope of a curve... (slope= "rate" of change)

"Fancy term" for addition ... Adding "area" under a curve into s…

Roots

Non Differentiable functions

undefined slope or vertical tangent line.

Derivative

Slope of a curve... (slope= "rate" of change)

natural numbers (N)

counting numbers

positive integers

whole numbers

numbers that we naturally use to count

numbers that we naturally use to count

numbers that we naturally use to count

numbers that we naturally use to count, including 0

natural numbers (N)

numbers that we naturally use to count

counting numbers

numbers that we naturally use to count

Average Velocity Equation

Secant Line

Instantaneous Velocity

Instantaneous Velocity equation

msec= (s(t1) - s(t0)) / (t1 - t0)

any line joining two points on a curve

The instantaneous velocity is called the limit

(limit,t->1) ((s(t) - s(t1)) / (t - 1))

Average Velocity Equation

msec= (s(t1) - s(t0)) / (t1 - t0)

Secant Line

any line joining two points on a curve

Division by zero is

A function is well defined when

Definition of the absolute value of a…

Definition of principle and truth

UNDEFINED

we get exactly one correct answer

abs(th)={th IF th is greater than or equal to zero... {-th IF t…

nroot(th)^n is equal to th. (You get what's inside when raise…

Division by zero is

UNDEFINED

A function is well defined when

we get exactly one correct answer

vertical shift

Horizontal shift

vertical stretching and shrinking

horizontal stretching and shrinking

f(x)+c is up... f(x)-c is down

f(x-c) is to the right... f(x+c) is the left

Cf(x) if C is greater than 1 than stretch... if C is less than…

f(Cx) if C is greater than 1 it shrinks... if C is less than 1…

vertical shift

f(x)+c is up... f(x)-c is down

Horizontal shift

f(x-c) is to the right... f(x+c) is the left

lim... x→4⁺

lim... x→4⁻

lim... x→4⁻ ... and ... lim... x→4⁺ are not equal

the two sided limit

Values getting closer to 4 ... approaches 4 in a positive direct…

going in the opposite direction... negative direction (3,2,1,0,-…

4 does not exist :(

for a limit to exist, both one sided limits have the same val…

lim... x→4⁺

Values getting closer to 4 ... approaches 4 in a positive direct…

lim... x→4⁻

going in the opposite direction... negative direction (3,2,1,0,-…

function

domain

f(x)

codomain

a rule that assigns to each element 'x' in a set 'D' exactly…

set of all possible inputs for a function f

value of f at x, is read as 'f of x'

set of all possible values of 'f(x)'

function

a rule that assigns to each element 'x' in a set 'D' exactly…

domain

set of all possible inputs for a function f

Average velocity

Absolute value

Direct substitution property (limits)

(If a function (f) is) continuous on.…

Change in position/ change in time

|a| distance between a and 0 on a number line: always positiv…

If (f)is a polynomial or a rational function and (a) is in th…

Continuous at every number in the interval.

Average velocity

Change in position/ change in time

Absolute value

|a| distance between a and 0 on a number line: always positiv…

Pythagorean Identity for sin and cos

Pythagorean Identity for tan and sec

Double Angle Identity for sin

Double Angle Identity for cos

sin²θ + cos²θ = 1

tan²θ + 1 = sec²θ

sin(2θ) = 2sinθcosθ

cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Pythagorean Identity for sin and cos

sin²θ + cos²θ = 1

Pythagorean Identity for tan and sec

tan²θ + 1 = sec²θ

Testing for x-axis symmetry

Testing for y-axis symmetry

Testing for origin symmetry

Finding y-intercepts

Substitute (x, -y) into the original equation and see if you…

Substitute (-x,y) into the original equation and see if you e…

Substitute (-x, -y) into the original equation and see if you…

Substitute x = 0 into the equation and find y.

Testing for x-axis symmetry

Substitute (x, -y) into the original equation and see if you…

Testing for y-axis symmetry

Substitute (-x,y) into the original equation and see if you e…