Determine one-on-one functions and thier inverse

Determine if the funtion is a one-on-one function. If so, then list the inverse function of the coordinates by switching the coordinates: f={(3,2),(8,6),(2,4),(16,18)} Since each x-value cooresponds to a unique y value, and each y-value corresponds to a unique x value, it is a one-on-one function.
To find the inverse of the function, simply switch the coordinates of the ordered pairs: f^-1={(2,3),(6,8),(4,2),(16,17)}
Determine whether the following function is a one-on-one function. If so, find the inverse by switching inputs and outputs: Month of 2013:
(input) Sept. Oct. Nov. Dec.
% rate of smokers in MI
(output): 45, 45, 40, 42
The function is not a one-on-one function. Each output of the table DOES NOT correspond to a unique input. The output 45 corresponds to both inputs Sept. and Oct. Due to the fact that this is not a one-on-one function, there is no inverse.
Given the one-on-one function F(x)=x^3+8, find the following:
a. f(-4)
b. f^-1(-56)
For f(-4), substitute x=-4 into the original equation:
a. f(x)=x^3+8=(-4)^3+8=-56
b. f^-1(-56)=-4 (you do not need to necessarily have to solve for f^-1)
Find the inverse of the one-on-one function: f(x)=x-6/4 First, replace f(x) with y so that the function reads Y=X-6/4. Next, interchange x and y so that the function now reads x=y-6/4. Now solve for y: y=4x+6 so f^-1(x)=4x+6
Find the inverse of the one-on-one function: f(x)=7/4x+3 f^-1(x)=7-3x/4x (Don't forget to flip the sign from positive to a negative)
Find the inverse of the one-on-one function: f(x)=x-7/13 Replace f(x) with y so that y=x-7/13. Then interchange x and y so that the function now reads x=y-7/13. Solve for y to get your final answer: f^-1(x)=13x+7
Applying the horizontal line test on the graph of a function serves what purpose? To determine if the graph is a function of a one-on-one function. If the horizontal line (horizontal line test) intersects the graph of a function only one time, then the function is in fact a one-on-one function.

Vanderbilt University Final Exam PSY 2530

Question Answer
Reliability/Validity Reliability-consistency/repeatability of a measure; three types-test retest, parallel forms, internal consistency
Validity- accuracy, does the measure measure what it purports to? Three types-content, criterion-related, construct
Index of reliability Empirical- upper bound expectation of what you can expect your measure to correlate w/ anything
Theoretical- correlation of scale and a perfect measure of the attribute it assesses
Correction for attenuation A way to estimate the correlation between the underlying TRUE scores because there is always some amount of measurement error (unreliability) so this is a way to correct for that error
Standard error of measurement SD of observed scores around the true score, increasing reliability shrinks CI’s
Internal consistency reliability Function of intercorrelation of items and how many Higher correlation&More tests give higher intercorrelation ratio Degree to which all items measure a common characteristic of the person and are free from measurement error.
Coefficient alpha A type of internal consistency reliability, estimates the reliability of a single administration of a single test. Mean of all possible reliabilities test can display given by 1/2ing the test
KR20 Special case of coefficient alpha test of internal consistency, average of all possible split-half correlations with dichotomous (T/F) items
Spearman-Brown Prophecy formula Demonstrates how reliability of a test changes a function of test length, makes it possible to compute reliability estimate from a single test
Split-half reliability Special case of SBP, estimates internal consistency, splits test in half (even/odd etc) and makes it easier to compute the correlation when n=2
Test-retest reliability same test administered multiple times is reliable if the correlation between scores is high
Parallel forms reliability Extent to which two tests measure the same concepts at the same difficulty level
Cattell’s L-Data, Q-Data, T-Data In order to fully understand a person, test needs to contain Questionnaires (subjective), Test data (objective) and Life-record data (how many kids?)
Methods of scale construction Internal-theoretical, items in this scale should be highly correlated
External-based on a criterion referenced group’s performance
Intuitive- comes from your head, two types
Rational-from you head (informal) and Theoretical (from formal theory)
Ceiling effect Has a – skew, happens when more people get a high (ceiling) score
Floor effect Has a + skew, happens when more people get a low (floor) score
Ecological validity Methods, materials, and setting of study approximate the real-world which is being examined, observed behaviors reflect what occurs in natural settings
Test bias Systematic over/under prediction that compromises accuracy of inferences
Trait by treatment interaction Determining which treatment is best by first determining what level you are at on trait
Radex Made up of simplexes and circumplexes map different tests by complexity and content. Items next to one another in same circle =similar complexity different content while items follow the same line out from the middle have similar content but diff complex
Circumplex The circle part of the radix, items in same circumplex have different content @ same complexity level
Simplex Lines radiating out from radix, items in same simplex, have same content @ different complexity levels, complexity increases as you move into center
Holland’s hexagon Six themes of vocational interests that represent 6 different types of individuals and 6 types of work environments, Realistic, Investigative, Artistic, Social, Enterprising, Conventional (RIASEC)
Self-directed search The test to determine which 3 themes of Holland’s hexagon one scores highest on, which gives them a summary code (RIA) that corresponds with a list of occupations. Designed to be used for career exploration w/o a career counselor
Positive and Negative Affect A dichotomous scale. Positive affect ranges from Joy (high) to depression (low)
negative affect from anxiety (high) to relief (low) +/- reinforcement/punish moves you from one quadrant to another. People who have high – and low + are seen for depression
Satisfaction/Satisfactoriness both necessary for determining tenure
Satisfaction-corresponds with interests, needs, and reinforcement in environment
Satisfactoriness- corresponds between ability and actual job requirements
Personality styles (4) basic ways individuals respond
Celerity-quickness of response interacting with environment
Pace-level of effort typically expended in interaction w/ environment
Rhythm-pattern of pace
Endurance-likelihood of maintaining interaction w/ environment
Meta analysis Combining Lots of findings from different samples and populations on same construct to get more precise CI on effect size or correlation, allows to generalize to larger phenomenon
Validity generalization Capacity of an instrument to be generalized to other populations
Formative evaluation Assessment techniques that guide the course of instruction
Summative evaluation Formal assessments are used after instruction is completed to summarize what students have learned
Halo errors categorize individual on a small number of salient observations and apply that general impression to all traits, positively or negatively
Generosity errors Human tendency to rate someone higher than they deserve because of unwillingness to mark someone as average or below average even
Response set Source of error, A tendency on part of test taker to approach test in manner that distorts test (saying yes too much because it might sometimes apply etc)
Social desirability Source of error, category of response sets with Tendency to choose responses that they believe are more socially accepted
Projective hypothesis Assumption that core concerns/conflicts color every perception and action
for projective assessment when give an ambiguous stimulus to a person, they will project what is happening with them, a way to see what people are thinking about (ink blots etc)
Validity scales (including VRIN and TRIN from Katie’s lectures) A subscale of a test designed to assist in judgments regarding how honestly the test taker responded and whether or not observed responses were products of response style, carelessness, deliberate efforts to deceive, or unintentional misunderstanding.
Index scores Allow for comparisons w/ same aged peers, Mean=100, SD=15
Wechsler scales of intelligence 4 index score=full scaleIQ
VCI-verbal comprehension
PRI- perceptual reasoning removes processing
General ability index-reasoning/comprehension
WMI- working memory
PSI- processingspeed
Cognitive Processing Index-relies on speed efficiency
Confidence interval If we repeat the test over and over, their score will be included _% of the time
Flynn effect Observed IQ increase of 3 points/decade during 20th century, greatest effect in lower portion of IQ distribution (better nutrition, parental literacy, test sophistication)
What are two Validity scales from MPQ? VRINvariable response inconsistency SIMILAR items endorsed opposite (feel good-T, feel great-F) Highscore=random
TRINTrue response inconsistency OPPOSITE items endorsed same(feel good-T,feel bad-T) High score=all true Low=all false (<30, >70 can’t use)
(VCI, PRI, WMI, PSI, FSIQ, GAI, CPI)? Verbal comprehension+Perceptual reasoning=General ability indes
Working memory+Processing speed=cognitive processing indes
=Full scale IQ
Discuss the psychological significance of positive and negative affect. Individual can be placed on graph at any point in time depending on their mood, individuals with high – affect and low + affect are seen for depression typically. Positive and negative reinforcement and punishment can move you around the graph
How does the model of talent development discussed in class functions to predict job/career tenure? Matches interests and abilities to determine how satisfactory an individual would be in in a position and how high his satisfaction would be, if matched correctly, should predict job tenure. Puts = stress on individual and the environment.
Discuss two ways in which ability tests can be psychologically close (or covary). In reference to the Radex, they can be highly correlated (physically close ) with similar levels of complexity (on same circumplex) or similar content (same simplex) Complexity increases as you move towards the center.


Question Answer
Øòî å äðîïêà? Äðîïêà å äåë îä öåëî.
Çàïèøè ãè äðîïêèòå ñî áðîåâè:
-åäíà ïîëîâèíà
-åäíà ÷åòâðòèíà
-åäíà îñìèíà
Êîëêó å åäíà ïîëîâèíà îä:
Êîëêó å ÷åòâðòèíà îä:
Êîëêó å îñìèíà îä:
Êîëêó å ïîëîâèíà îä 24?
Êîëêó å òðåòèíà îä 24?
Êîëêó å ÷åòâðòèíà îä 24?
ÊÎëêó å øåñòèíà îä 24?
Êîëêó å îñìèíà îä 24?
Âî íàøåòî îääåëåíèå èìà 20 ó÷åíèêà. Ïîëîâèíà îä íèâ ñå îäëè÷íè ó÷åíèöè. Êîëêó ó÷åíèöè ñå îäëè÷íè? Îäãîâîð: Äåñåò ó÷åíèöè ñå îäëè÷íè
Íàñòàâíè÷êàòà ïîñòàâèëà 12 çàäà÷è ïî ìàòåìàòèêà. Îä íèâ ó÷åíèöèòå ðåøèëå åäíà ÷åòâðòèíà. Êîëêó çàäà÷è ðåøèëå ó÷åíèöèòå? Îäãîâîð: Ó÷åíèöèòå ðåøèëå 3 çàäà÷è:
Ìàðòà ÷èòà êíèãà îä 64 ñòðàíèöè. Ïðâèîò äåí òàà ïðî÷èòàëà åäíà îñìèíà îä êíèãèòå. Êîëêó ñòðàíèöè ïðî÷èòàëà Ìàðòà? Îäãîâîð: Ìàðòà ïðî÷èòàëà 8 ñòðàíèöè.
Âî ó÷èëíèöàòà èìà íà 6 ïîëèöè ïî 6 êíèãè.Åäíà ÷åòâðòèíà îä íèâ ñå ïî ìàòåìàòèêà. Êîëêó êíèãè ñå ïî ìàêåäîíñêè ¼àçèê? Ðåøåíèå:(6×6)-(6×6:4)=36-9=27

Expression and Equation Words

Term Definition
Algebraic Expression a mathematical phrase with no equal sign
Addition Property of Equality adding a number to its opposite will give you zero
Coefficient a number in front of a variable
Constant a number without a variable
Division Property of Equality dividing a number by itself will give you one
Equation a mathematical sentence with an equal sign
Evaluate to replace variables with their given values and simplify
Inverse Operations opposite operations that "undo" each other
Like Terms terms with the same variable to the same power
Multiplication Property of Equality multiplying a number by its reciprocal will give you one
Reciprocal flipping a fraction over
Simplifying an Expression to combine like terms and perform operations, getting the expression down to its simplest form
Solution the value of a variable when solving an equation
Subtraction Property of Equality subtracting a number from itself will give you zero
Substitution replacing a variable with its given value, used to check equations
Term parts of an expression separated by plus and minus signs

Module 24 – Logarithmic Functions and Properties of Logarithms

Term Definition
log4 16=2 log4 16=2 is just another way of saying 4 to the second power is equal to 16.
logb x=y means… X=b^Y
Write as an exponential equation.
log5 25=2
Write as an exponential equation.
log7 x=5
Log2v2=1/2 This means 2^1/2=v2.
True or false:

The base can be equal to 1 and greater than zero.

False. the base can be greater than zero but not equal to one.

log5 x=3

log5 x=3
True or false:
logb b^x=x
What is the Product Property of Logarithms? logb xy=logb x+logb y
True or false:
logb x/y=logb x-logb y

Review of Math Terms

Term Definition
Proportion An equation stating that two ratios or rates are equivalent.
Ratio A comparison between two quantities.
Origin The point at which the x-axis and y-axis intersect. The _____ is at the point (0,0).
Simple Interest The amount of money paid or earned for the use of money.
The formula for _____ ______ is I=prt.
Sales Tax An additional amount of money charged on items that people buy.
Percent of Change A ratio that compares the amount of change to the original amount. Examples of _____ _____ ____ include markup, discount, percent of increase, and percent of decrease.
Additive Inverse Two integers that are opposites. The sum of an integer and its _________ _________ is zero.
Graph The process of placing a point on a number line or coordinate plane at its proper location.
Zero Pair The result when one positive counter is paired with one negative counter. 8 and -8 is an example of a _____ _____.
Bar Notation In repeating decimals, the line placed over the digits that repeat.
Least Common Denominator The least common multiple of the denominators of two or more fractions.
Like Fractions Fractions that have the same denominator.
Sequence An ordered list of numbers.
Algebraic Expression An expression that contains numbers, variables, and at least one operation.
Constant A term that does not contain a variable.
Two-Step Equations An equation having two different operations.
Equivalent Equations Two or more equations with the same value.
Multiplication Property of Inequality When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed in order for the inequality to remain true.
Acute Angle An angle with a measure greater than 0, but less than 90.
Complementary Angles Two angles are _______ if the sum of their measures is 90.
Right Triangle A triangle having one right angle.
(A triangle having one angle that is 90 degrees.)
Circumference The distance around a circle.
Diameter The distance across a circle through its center.
Pi The ratio of the circumference of a circle to its diameter. The estimated value for ____ is 3.14.
Probability The chance that some event will happen. It is the ratio of favorable outcomes to the possible outcomes.
Sample Space The set of all possible outcomes of a probability experiment.
Compound Event An event consisting of two or more simple events.
Vertex The vertex of an angle is the common endpoint of the rays forming the angle.
Factor To write a number as a product of its factors.
Algebra A branch of mathematics that involves expressions with variables.

made on 4/21/14

description formula
euler's thereom F+V=E+2
surface area of a prism SA= 2B+Ph
lateral area of prism LA= Ph
surface area of a right cylinder SA= 2?r^2 + 2?rh
lateral area of a right cylinder LA= 2?rh
surface area of an oblique cylinder SA= 2?r^2 + 2?rl
surface area of a regular pyramid SA= B + (Pl)/2
surface area of a cone SA= ?r^2 + ?rl
volume of a cube V= s^3
volume of a prism V=Bh
volume of a cylinder V=?r^2h
volume of a pyramid V=Bh/3
volume of a cone V= (?r^2)h/3=Bh/3
volume of a frustum V= (1/3)h(B1 + B2 + vB1B2)
surface area of a frustum SA= ?(R+r) v((R-r)^2+h^2) + ?R^2 + ?r^2
SA= ?(R+r)L + ?R^2 + ?^2
surface area of a sphere SA= 4?r^2
surface area of a hemisphere SA= 3?r^2
volume of a sphere V= (4/3)?r^3
volume of a hemisphere V= (2/3)?r^3
what is a great circle the intersection formed when a plane contains the center of a sphere
whats a hemisphere the two congruent halves of a sphere that contain the great circle
whats a diameter a chord that contains the center

Geometric Figures

Question Answer
Two opposite angles formed by the intersection of two lines. Vertical Angles
Angles that have the same measurement Congruent
Two angles that share a common vertex, common side, and do not overlap Adjacent
Two angles that have a sum of 90 degrees complementary
Two angles that have a sum of 180 degrees Supplementary
All angles are acute in the triangle Acute Triangle
There is 1 right angles in the triangle Right Triangle
There is 1 obtuse angle in the triangle Obtuse Triangles
Less than 90 degreeAcute angle Acute angle
Exactly 90 degreesRight angle Right angle
Greater than 90 degreesObtuse angle Obtuse angle
A triangle with no congruent sides Scalene triangle
A triangle with two congruent sides Isosceles triangle
All sides are congruent in the triangle Equalateral
Sides with the same length Congruent sides
Representation of objects that are too big to draw in actual size Scale drawing/model
The ratio that compares the measure of the model to the measure of the actual object Scale
A scale written as a ratio with no units in simplest form Scale factor
A flat surface that goes on forever in all directions plane
Lines that fall on the same plane coplanar
Lines that will never intersect parallel
Line where two planes intersect Edge
Point where 3 or more planes intersect vertex
a flat surface face
a line segment whose endpoints are vertices that are neither adjacent nor on the same face Diagnol
A 3D figure with 2 parallel congruent circular bases connected by a curved surface Cylander
A 3D figure with one circular base connected by a curved side to one vertex Cone

6th Grade Math: Linear Equations

Question Answer
A math problem that combines variables, numbers, and at least one operation; example: d + 5 Algebraic Expression
The numerical factor for a multiplication expression; example: 4 in the term 4x Coefficient
What is another name for rate? Speed
An equation that shows the relationship among different quantities Formula
An equation that has two different operations Two-step Equation
The distance around a geometric figure Perimeter
The measure of the surface within a geometric figure Area
An equation, that when graphed, creates a straight line Linear Equation