Algebra 1 Vocabulary FLVS
Rational Functions
A function that can be represented using fractions of polynomials
Linear Function
A function that is defined by a linear expression and written using function notation
Exponential Function
A function that is defined by an exponential expression and written using function notation, and the variable is an exponent; example, f(x) = abx
Scatter Plot
A graph on which two different sets of data are plotted using coordinates
Line of Best Fit
A line drawn through the points on a scatter plot to summarize the relationship between the two sets of data
Square Roots
A number times itself equals the square under the radical sign
Coefficient
A number which multiplies a variable; example: 3x, 3 is the coefficient
Absolute Value
A number's distance from zero on a number line; examples: |-3| = 3 and |3| = 3; both numbers are 3 units away from zero
Composite Function
A process in which the output of one function is the input for the next function: example: f[g(x)]
Combining Like Terms
A process of combining terms that have identical variable parts.
Completing the Square
A process that allows one to rewrite a quadratic trinomial in general form or standard form into vertex form
Zero Exponent Property
A property that says any number (except 0) with an exponent of 0 is defined to equal 1; a0 = 1
Negative Exponent Property
A property that says any number raised to a negative power equals to the reciprocal of the positive exponent of the number; a^-2=1/a^n
Rational Exponent Property
A property that says fractional powers, or where a number is raised to a fraction, can be converted to a radical; the numerator becomes the exponent, and the denominator becomes the index of the radical; x ^m/n = n square root of x^m
Zero product Property
A property that says that zero times anything equals zero. If ab = 0, then either a or b (or both) has to be zero. If a polynomial has factors multiplied together and the product is zero, then at least one of them has to be zero.
Power of a Quotient Property
A property that says to find a power of a quotient, find the power of each part of the quotient, and then divide by canceling common factors; (x/y)^n = x^n/y^n
Power of a Power Property
A property that says to raise a power to a power, multiply the exponents; (am)n = am • n
Power of a Product Property
A property that says to raise a product inside parentheses to a power, apply that power to each factor inside the parentheses; (ab)m = ambm
Vertex Form of a Quadratic Equation
A quadratic equation of the form y = a(x − h)2 + k where (h, k) is the vertex of the parabola
Standard Form of a Quadratic Equation
A quadratic equation of the form y = ax2 + bx + c, where each term is in decreasing order of degree
Relation
A relationship that pairs input values with output values
Monofilament
A single, untwisted, synthetic filament
Extraneous Solution
A solution of the simplified form of the equation that doesn't satisfy the original equation
Controlled Study
A study on two comparable groups; the groups are given different sets of experiences, and the outcomes are compared
Arithmetic Series
A sum of a list of numbers that are separated by a common difference
Geometric Series
A sum of a list of numbers that are separated by a common ratio
Variable
A symbol, usually a letter, which takes the place of an unknown value
Consistent System
A system of equations that has at least once solution; a pair of intersecting lines or same lines are consistent systems
Inconsistent System
A system of equations that has no solution is called an inconsistent system; parallel lines are an inconsistent system
Two-way Frequency Table
A table where each cell in the table has the frequencies of two categories of data
Vertical Line Test
A test that determines if the graph of something is a function—if the graph crosses any vertical line at more than one point, the relation is not a function
Correlation Coefficient
A value that describes how closely the numbers in the data set are related
Factor
A value that is multiplied by another value to get a product
Axis of Symmetry
A vertical line that passes through the vertex of the parabola
Box Plot
A visual that divides a list of data into four sections called quartiles
Bar Graph
A visual that shows data that appear in categories
Histograms
A visual that shows data that appear in ranges (numerical data)
Dot Plot
A visual that shows the frequency of which something occurs; in a dot plot, the number of dots over a number line tells how many times that number occurs in the data
Point-Slope Form
A way of writing a linear equation using the slope and any point on the line y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line
Quadratic Equation
An equation of the form y = ax2 + bx + c, where "a", "b" and "c" are real numbers, and "a" cannot be zero
Rational Equations
An equation represented using fractions of polynomials
Radical Equation
An equation that has a variable in the radicand
Literal Equations
An equation that has two or more variables
Function Rule
An equation that represents an output value in terms of an input value
Proportion
An equation that states two ratios are equal
Linear Equation
An equation whose graph is a straight line, where the highest exponent on the variables is 1
Rational Exponent
An exponent expressed as a fraction
Prime Expression
An expression that does not have a common factor in the coefficients or the variables and cannot be factored in any other way
Linear Inequalities
An inequality that can be expressed as an equation and it graphed as a line with areas of inclusion and exclusion
Perfect Square
An integer that can be made by multiplying two of the same integers together
Closure Property
An operation is considered closed over a set of numbers or a system when two or more elements of the same set are combined by that operation and the result is also an element of the set.
Sequence
An ordered list of numbers, objects, or events that often form a pattern
Term
One letter, number, or product of letters and numbers, also known as a monomial
Terms
One letter, number, or product of letters and numbers, also known as a monomial
Monomial
One letter, number, or product of letters and numbers, also known as a term
Parallel Lines
Parallel lines have the same slope, are traveling in the same direction, and will never cross, but have different y-intercepts
Nonviable
Not a possible solution to the question being asked
Inequality
Not equal, more than, less than, not the same
Function Notation
Notation that is used to represent a function; namely f(x), read f of x
Elements
Numbers or objects in a set
Consecutive Integers
Numbers right beside each other on a number line; for example: 1, 2, 3, ... or -5, -6, -7, ...
Dividend
Numerator, or what is being divided into
Consecutive Odd Integers
Odd numbers right beside each other on a number line; for example 1, 3, 5, ... or -3, -5, -7, ...
Exponent
Tells how many times the base is used as a factor, or the number of time the base is multiplied by itself
Like Terms
Terms with the exact same variables with the exact same exponents for the variables
End Behavior
The behavior of the graph of as x approaches positive infinity or negative infinity
Run
The horizontal change of a line from one point to another
Rate (interest)
The interest rate you are given on the money you borrow
Intersection
The intersection of two or more sets is made up of the elements that the sets share; the term intersection is represented using an upside down symbol which looks like ∩
Greatest Common Factor (GCF)
The largest positive integer that divides without a remainder into two or more chosen integers
Maximum (of data set)
The largest value in a data set
Boundary Lines
The line in the graph of an inequality that divides the plane into two parts—one side representing points that are solutions to the inequality and one side representing points that are not solutions to the inequality; the lines are dashed or solid based on the inequality symbol
Central Tendency
The measure of the "middle" of a set of data; common measures are the arithmetic mean, median, and mode
Interquartile Range (IQR)
The middle half of the data; it is a measure of how widely the middle half of the data is spread around the median
First Quartile
The midpoint of the lower half of the data when the data is listed in numerical order
Lower Quartile
The midpoint of the lower half of the data when the data is listed in numerical order; also known as the first quartile
Reciprocal
The multiplicative inverse of a number; for example, 2 divided by 3 is the reciprocal of 3 divided by 2
Radicand
The number or expression contained under a radical sign
Base
The number or quantity being raised to a power
Median
The number that falls in the middle when the data are ordered; when there is an odd number of terms, it is the middle term; when there is an even number of terms, it is the mean of the two middle terms
Exponential Decay
When the graph of an exponential function decreases from left to right; the base of the exponential expression must be between 0 and 1
Exponential Growth
When the graph of an exponential function increases from left to right; the base of the exponential expression must be greater than 1
Compound Interest
When the interest rate (or rate of growth) is applied to the principal and all other interests earned to that point
Simple Interest
When the interest rate (or rate of growth) is applied to the principal only
Algebraic Ratio
When the numerator, denominator, or both parts of a ratio contains a variable expression
Standard Form
When the polynomial is listed with each term in decreasing order of degree
Independent System
When two lines do not share all of the same points, such as parallel lines or intersecting lines
Intercept
Where the line you are graphing intersects the axes of the coordinate plane
Law of Negative Exponents
a-n = 1/a^n . The multiplicative inverse of the base raised to the positive opposite of the power.
Product of Powers Property
am • an = am+n. To multiply powers with like bases, add the exponents.
Probability
How likely an event is to occur
Real Number
A number that is rational or irrational; examples: -4, , 1/3, 3.2
Horizontal Lines
Lines that have a slope equal to zero
Vertical Lines
Lines that have a slope that in undefined
Rise
The vertical change of a line from one point to another
Compound Inequality
Two inequalities joined by the word "and" or the word "or"
Difference of Two Squares
Two perfect squares being subtracted
PEMDAS
"Please Excuse My Dear Aunt Sally" is a mnemonic device reminding you that the order of operations is Parentheses, Exponents, Multiplication or Division, and finally Addition or Subtraction
Explicit Formulas
A formula that can generate any term in a sequence just by inputting the term number
Recursive Formula
A formula that can generate terms one at a time by relating the term to one or more previous terms
Rational Expression
A fraction containing polynomials
Equal Sign
=; Tells you that what is on the left side of the equation equals what is on the right side of the equation
Inequality Symbols
> greater than, < less than, ≥ greater than or equal to, ≤ less than or equal to
Parabola
A U-shaped curve, created by a quadratic equation
Statistics
A branch of mathematics that views numbers as data sets and teaches how to use a variety of methods to organize, interpret, and analyze these numbers to make informed decisions
Set
A collection of numbers or objects
Ratio
A comparison of two numbers by division
Constant Function
A constant function is a linear function of the form y = b, where b is a constant; it is also written as f(x) = b; the graph of a constant function is a horizontal line
Outlier
A data point that is significantly larger or smaller than the other values
Standard Form of a Linear Equation
A linear equation in which the x term and the y term are written on the same side of the equal sign, with the constant (number-only term) on the other side; A, B, and C are integers; and A is positive; Ax + By = C
Arithmetic Sequence
A list of terms that share a common difference; the difference between the consecutive terms is constant
Geometric Sequence
A list of terms that share a common ratio; each term is found by multiplying or dividing the same value from one term to the next
Polynomials
A mathematical expression that has: a) one or more terms, b) variables with only positive, whole number exponents, and c) no variables in the denominators of each term
Function
A mathematical relationship in which each input value is paired with exactly one output value
Equation
A mathematical statement containing an equal sign to show that two expressions are equal
Standard Deviation
A measure of spread to allow for comparisons to the overall data set; found by finding the sum of the square of the differences of each data point from the mean, dividing it by the number of data points, and square rooting that value
Sigma Notation
A method of writing a long series of numbers in an abbreviated format; also known as summation notation
Numerical Expression
A number or a group of numbers that are added, subtracted, multiplied, or divided; example: 4 + 6 is a numerical expression
Rational Number
A number that can be expressed as a ratio (fraction) of two numbers; this includes decimals that terminate or repeat; examples: , 4/5 -14, 2.1, √4 (square root of 4 is 2, and is rational)
Irrational Number
A number that cannot be expressed as a ratio (fraction) of two numbers; this includes decimals that never stop or repeat; examples: √5, 3.2516...
Slope-Intercept Form
A way of writing a linear equation where the y-variable is isolated on one side of the equation. Slope-intercept looks like y = mx + b, where m equals the slope and b equals the y-intercept.
The Statistical Process
A way to collect, organize, understand, and represent data; a standardized process so that analysis can be compared and informed decisions can be made using comparable data
Whole Number
All positive whole numbers including zero; this category does not include any negative whole numbers; examples: 0, 3, 6
Natural Number
All positive whole numbers, not including zero; examples: 4, 7, 9
Algebraic Equation
An algebraic equation is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc. and also contains an equal sign that sets two algebraic expressions equal to each other; example: x + 4 = 9 is an algebraic equation
Algebraic Expression
An algebraic expression is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc; example: x + 4 is an algebraic expression
Quotient
Answer to the division problem
Infinitely Many Solutions
Any ordered pair that satisfies one of the equations or inequalities will also satisfy the other equation or inequality; the equations describe the same line, or the inequality has the same border line
Reflexive Property
Anything is equal to itself; same numbers or terms on both sides of the equal sign, 5 = 5
Mondrian Art
Art that uses vertical and horizontal lines with geometric fields of colors
Prime Factorization
Factoring a number into its prime factors only
System of Equation
Collection of two or more equations
Nonlinear System of Equations
Collection of two or more equations where at least one equation is not linear
Divisor
Denominator, or what is being divided by
Transformation
Describes the change in a figure
Graphical Representation
Displaying an equation, point, or segment on a graph
Simplify
Distributing, combining like terms, etc.
Term of a sequence
Each individual number, object, or event in a list of a sequence is called a term
Elimination Method
Eliminating one of the variables when combining the two equations
Rationalizing the Denominator
Eliminating the square root (radical) from the denominator
Degree of a Polynomial
Equal to the degree of the term with the highest degree
Consecutive Even Integers
Even numbers right beside each other on a number line; for example 2, 4, 6, ... or -4, -6, -8, ...
Infinite
Extending to infinity or indefinitely
Cross Multiply
Finding the cross products of two ratios
Greatest Perfect Square Method
Finding the largest perfect square factor of a number or expression that is not a perfect square
Transitive Property
For any real numbers a, b, and c if a = b, and b = c, then a = c. Three parts: the first statement relates to the second, which relates to the third.
Distributive Property
For every real number a, b, and c, a(b + c) = ab + ac or a(b - c) = ab - ac
Addition Property of Equality
For every real number a, b, and c, if a = b then a + c = b + c
Multiplication Property of Equality
For every real number a, b, and c, if a = b then a(c) = b(c)
Subtraction Property of Equality
For every real number a, b, and c, if a = b, then a - c = b - c
Division Property of Equality
For every real number a, b, and c, if a = b, then a ÷ c = b ÷ c
Inverse Functions
Functions whose compositions simplify to x; for example, if f(x) and g(x) are inverses of each other, then f(g(x)) = g(f(x)) = x
Associative Property of Addition or Multiplication
Grouping symbols do not affect the outcome. Numbers can be associated by using parentheses or brackets in an addition or multiplication problem and it does not change the solution.
Factoring by Grouping
Grouping terms into pairs before factoring a GCF from each group
Guess and Check Method
Guess a solution and check to see if it works by substituting it into the equation
Accuracy
How closely a given set of values are compared to the expected value
Substitution
If two quantities are equal, one quantity may be put in the place of the other quantity and the value of the expression does not change
Carbon Footprint
Impact on the environment
Leading Coefficient
In a polynomial in terms of x, the coefficient in front of the x term with the highest degree in the polynomial
Conjunction
Inequalities joined by the word "and"
Disjunction
Inequalities joined by the word "or"
Horizontal Asymptote
Invisible horizontal lines that a rational function approaches, yet does not cross, when graphed
Vertical Asymptote
Invisible vertical lines that a rational function approaches, yet does not cross, when graphed
Substitution Method
Isolating one variable in one of the equations and substituting it into the other equation
Opposite Operation
Performing the inverse operation to solve an equation; example: the inverse of addition is subtraction; the inverse of multiplication is division
Perpendicular Lines
Perpendicular lines have opposite reciprocal slopes and always cross at a 90o angle; for example, a line having slope 2 is perpendicular to a line having slope -1/2
Integer
Positive and negative whole numbers including zeros; this category does not include any fractions or decimals; examples: -2, 0, 4
Viable
Possible solution to the question being asked
Mono-
Prefix for words involving only one thing
Tri-
Prefix for words involving three things
Bi-
Prefix for words involving two things
Absolute Value Inequalities
Problems that involve ranges with inequalities
Properties of Equality
Properties that state that two or more items are the same
Real Number System
System of numbers that includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers
Equivalent Systems
Systems of equations that have the same solutions
Constraints
Restrictions placed on a variable depending on a real-world situation
Mean Absolute Deviation
Shows the average distance of the data points from the mean; f found by finding the sum of the differences of each data point from the mean and dividing it by the number of data points
Joint Frequency
Shows the data for each two-category response and occurs in the body of the table; found by reading from the inner cells of a two-way frequency table
Restriction
Stating that a variable cannot equal a specific number or set of numbers
Grouping Symbols
Symbols that signify two or more things are grouped together; parentheses ( ) or brackets [ ]
Parameter
The constant or the limits within the problem
Residuals
The difference between the actual values and the predicted values; normally used to determine the accuracy of the line of best fit created on a scatter plot
Range (of data set)
The difference between the largest and smallest values in a data set
Difference
The difference between two numbers (subtraction)
Rate of Change, or Slope
The difference of the y-values divided by the difference of the x-values
Slope
The difference of the y-values divided by the difference of the x-values
Discriminant
The expression located under the radical in the Quadratic Formula that can determine the number and type of solutions to a quadratic equation
Perfect Square Trinomial
The first and last terms of a trinomial are perfect squares and the middle term is equal to two times the product of the square roots of the first and last terms
Order of Operations
The order in which mathematical operations should be done: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).
Commutative Property of Addition or Multiplication
The order in which you perform an operation does not affect the outcome. Numbers can move around or commute in an addition or multiplication problem and it does not change the solution.
Symmetric Property
The order on either side of the equal sign does not matter. One side of the equation is the same as the other (think symmetrical) 3 = 2 + 1, 2 + 1 = 3
Principal
The original amount you borrow
Parent Function
The original function or function you start with
Solution to a System of Equations
The pair of values that make both equations true
X-Intercept
The point where a graph intersects the x-axis; the value of x when y = 0
Y-intercept
The point where a line crosses the y-axis; the value of y when x = 0
Domain
The possible input values (x values)
Range
The possible output values (y-values)
Function Composition
The process of combining two functions by using the output of one function as the input in the second function
Joint Relative Frequency
The proportional values found in the interior of a relative frequency table
Slope of a Line
The ratio of the vertical change to the horizontal change between two points, represented in equations by m
Correlation
The relationship between two groups of data
Sum
The result of adding
Equality
The same
Negative Slope
The slope of a line is negative if the line runs from the top left to the bottom right; the moves for the slope should be opposite moves, either down and to the right or up and to the left
Positive Slope
The slope of a line is positive if the line runs from the bottom left to the top right; the moves for the slope should be either both in the positive direction (up and to the right) or both in the negative direction (down and to the left)
Undefined Slope
The slope of a vertical line
Least Common Multiple (LCM)
The smallest (least) multiple that the two numbers have in common (the same). Example, the LCM of 2 and 3: Multiples of 2 are 2, 4, 6, 8, 10, 12, etc. Multiples of 3 are 3, 6, 9, 12, 15, etc. The smallest multiple they have in common is 6.
Minimum (of data set)
The smallest value in a data set
Area
The space surface takes up, measured in square units
Quotient Property of Radicals
The square root of a quotient is equal to the quotient of the square roots.
Mean
The sum of the data points divided by the number of data points
Degree of a Term
The sum of the exponents on the variables in the term
Trinomial
The sum or difference of three terms
Binomial
The sum or difference of two terms
Radical
The symbol for a square root
Vertex
The turning point (minimum or maximum) of a parabola
Solution
The value for the variable that makes the equation true
Power
The value of a number or quantity raised to some exponent
Relative Frequency
The value of each cell shown as a ratio with respect to all of the data in a two-way frequency table; shows each frequency as a proportion of the whole data sample size
Average Rate of Change
The value that shows how much the range values have changed per unit in the domain for a specified interval in the domain
Marginal Frequency
The values calculated from the row and column totals in a two-way frequency table
Zeros of a Polynomial
The values of the input of a polynomial function that would make the function zero; appear as the x-intercepts on the graph of the polynomial
Marginal Relative Frequency
The values shown in the column and row totals of a relative frequency table
Maximum Point
The vertex of a parabola that opens down
Minimum Point
The vertex of a parabola that opens up
Upper Quartile
This is the midpoint of the upper half of the data when the data are listed in numerical order; also known as the third quartile
Third Quartile
This is the midpoint of the upper half of the data when the data is listed in numerical order
Conditional Relative Frequency
This value shows a frequency proportion for a given condition or category
Evaluate
To calculate the value of
Distribute
To deliver or pass something out
Expanded Form of an Exponent
To expand a power means to write the multiplication represented by the exponent
Least Common Denominator (LCD)
To find a Least Common Denominator (LCD), start by listing the first few multiples of each denominator. Stop when you find a multiple that they have in common. This is the LCD.
Associate
To group with something else
Commute
To move around
Transit
To move something around
Reflection
To see the exact opposite of something, like the reflection in a mirror
Isolate
To separate out from all other parts
Closed Circle
Used on number lines when graphing greater than or equal to or less than or equal to inequalities
Open Circle
Used on number lines when graphing greater than or less than inequalities
All Real Numbers
Used when solving an equation in which both sides of the equation are the same; all real numbers means that any real number would make the equation true
No Solution
Used when solving an equation or inequality in which the solution is false; no solution means that there is no possible value for x that would make the equation or inequality true
Prime
When a number can be evenly divided only by one and itself
Dependent System
When all of the solutions on one line are the same as the other line in a system; this would create the same line
Descending Order
When all of the solutions on one line are the same as the other line in a system; this would create the same line
Causation
When one set of data directly causes the other to occur
Rate
When one unit of measure changes in terms of another unit
