algebra 1 vocabulary

function notation

Writing algebraic variables as functions of other variables, like 𝑓(𝑥) = 4𝑥 (which is read "the function of 𝑥 equals 4𝑥," so basically f takes 𝑥 and multiplies it by 4).

linear function

when a graph is a straight line that increases or decreases at a constant rate .

perfect squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

perfect cubes

1,8,27,64,125,216,343

arithmetic sequence

A sequence where each term is the sum of the previous term and a common difference, 𝑑

clousure property

A set of numbers is said to be closed for a specific mathematical operation when the result obtained after performing the operation on two elements of the set always produces an element of the same set

equation

A statement that the values of two mathematical expressions are equal (indicated by the sign =)

variable

A symbol used to represent a quantity that can change

Intergers

Any positive or negative number, including zero but with no fractional or decimal part

Stretching a function

Multiplying a function by a coefficient greater than 1

x-intercept

On a graph, the value of 𝑥 at the point where the line crosses the 𝑥-axis; this happens when the value of 𝑦 is zero

y-intercept

On a graph, the value of 𝑦 at the point where the line crosses the 𝑦-axis; this happens when the value of 𝑥 is zero

leading coefficient

The coefficient of the leading term in a polynomial equation

AND inequality

The compound inequality is true only if both statements are true

degree of a polynomial

The highest degree of any monomial or term in the polynomial

maximum

The highest point (vertex) on a graph when a parabola opens down; the point where the graph changes from increasing to decreasing

vertex

The maximum or minimum point of a parabola

leading term

The monomial or term with the highest degree in a polynomial equation

Relative minumum

The point on a graph where the interval changes from decreasing to increasing

relative maximum

The point on a graph where the interval changes from increasing to decreasing

residual

The vertical distance between an actual data point and the predicted value of the function fitted to the data

Standerd form of a polynomial

When the monomial terms of a polynomial expression are organized in descending degree order from left to right

vertex form

Given 𝑎(𝑥−h)2+𝑘,(h,𝑘)is the vertex of a parabola

Histogram

A bar-style data display showing the frequency of data measured over intervals, rather than displaying each individual data value

box plot

A box and whisker diagram that display the five-number summary for a data set (minimum, first quartile, median, third quartile, and maximum values)

geometric sequence

A sequence of numbers in which each term is the product of the previous term and some real number

Parabola

A curved symmetrical U-shaped graph that is the graphic representation of a quadratic function; it may open up or down

constant

A fixed value within an equation or expression (a number or letter that stands for a fixed number)

recursive formula

A formula to solve for a term using the computation of all previous terms

explicit formula

A formula to solve for a term using the first term of the sequence and the fixed rule for the sequence

Dot Plot

A graphical representation where each data value is represented with a dot above a number line

slope

A measure of the steepness of a line or a section of a line calculated by connecting two points and dividing the change in the dependent values by the change in the independent values

factor

A number or quantity that when multiplied by another produces a given number or expression

1st quartile

A number representing the first 25% of the data

3rd quartile

A number representing the first 75% of the data

real numbers

A number that can be any of the following: natural numbers, whole numbers, integers, rational numbers, irrational numbers

coefficient

A number used to multiply a variable

OR Inequality

A pair of numbers used to locate a point or a location on a coordinate plane; the first number (usually x) tells how far to move horizontally and the second number (usually y) tells how far to move vertically

ordered pair

A pair of numbers used to locate a point or a location on a coordinate plane; the first number (usually x) tells how far to move horizontally and the second number (usually y) tells how far to move vertically

rate of change

A rate that describes how one quantity changes in relation to another quantity

rational number

A real number including those with a fractional or decimal part; it can be written in the form a/b, where a and b are integers

irrational numbers

A real number that cannot be written as a simple fraction (in the form a/b, where a and b are integers), and when written as a decimal, the decimals do not terminate, nor do they repeat

function

A relationship between input and output, where each input has a single output

coordinate plane

A two-dimensional surface on which points, lines and curves can be plotted ; it has two scales, called the x-axis (a horizontal number line) and y- axis (a vertical number line) and four quadrants with positive and negative numbers in both axes.

Input

A value assigned to the known variable in a function

dependent variable

A variable whose variation depends on that of another (output, range)

independent variable

A variable whose variation does not depend on that of another (input, domain)

axis of symmetry

A vertical line that goes through the vertex of a quadratic function and divides the parabola into two congruent halves, that are mirror images of each other(in𝑓 𝑥 =𝑎𝑥2 +𝑏𝑥+𝑐the axis of symmetry is𝑥=− 𝑏) 2𝑎

area model

A visual model for multiplication; a rectangular array used to find all the factor pairs of a number or an expression

vertical line test

A way to test if a graph represents a function: if a vertical line drawn anywhere on a graph hits the graph in more than one place, then the graph is not a function since this shows an input value, 𝑥, has more than one output value, 𝑦

Shifting function

Adding or subtracting a constant to the independent variable of a function will shift the function left or right; adding or subtracting a constant to/from the dependent variable will shift the function up or down.

Natrual Numbers

All positive integers greater than zero

Monomial

An algebraic expression consisting of one term

Polynomial

An algebraic expression consisting of one term or the sum of several terms that contain different powers of the same variable(s)

Trinomial

An algebraic expression consisting of three terms

Binomial

An algebraic expression consisting of two terms

skewed data

Data that have a long tail on one side or the other; a data set in which mean is greater or less than median

Mapping

Diagram that shows how the inputs of a function are related to its outputs

range

Distance between highest and lowest scores in a set of data.

Quartiles

Divides a sorted data set into four equal parts, so that each part represents KP . Of the data set; 25% of the data within a data set.

Transformation

It occurs when an operation is performed on the dependent or the independent variable

whole numbers

Positive integers greater than or equal to zero; whole numbers cannot be negative or fractions

Divsion Property of Equality

Property of equality that is used to divide the same quantity into both sides of an equation, creating a different, but equivalent, equation

MULTPLICATION PROPERTY OF EQUALITY

Property of equality that is used to multiply both sides of an equation by the same quantity, creating a different, but equivalent, equation

Negative Exponent Property

Property of equality that states that a number with a negative exponent should be moved to the other side of the fraction line and the exponent switched to positive

Addition Property of Equality

Property of equality that states that adding the same quantity to both sides of an equation creates a different (but equivalent) equation

Distributive Property

Property that states that multiplying a single term by two or more terms inside a set of parentheses yields an equivalent expression

Zero Product Property

Property that states that when the product of two or more factors equals zero, one or more of the factors must also equal zero

Evaluating a function

Replace (substitute) a number for the function's variable; finding the value of the expression for that number

inverse function

Reverses or undoes the action of another function by interchanging the dependent and independent variables of the function for an appropriate set of values of the dependent variable

Subtraction Property of Equality

Solving one of the equations for one of the variables, and then substituting the result into the other equation to have only one variable to solve for

Power of a Product Property

States that if there is more than one factor in parenthesis, with an exponent outside the parenthesis, then the exponent is distributed to every term in the parenthesis

Power of a Quotient Property

States that the power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately, before the division is performed

Product of Powers Property

States that the product of two powers with the same base is the base raised to the sum of the powers (exponents)

Quotient of Powers Property

States that the quotient of two powers with the same base is the base raised to the difference of the powers (exponents

Power of a Power Property

States that to find a power of a power, multiply the exponents

slope-intercept form

Takes the form of 𝑦 = 𝑚𝑥 + 𝑏 and represents the equation of a line with a slope of 𝑚 and and a 𝑦- intercept of 𝑏

average rate of change

The change in the value of a quantity divided by the elements in the interval or the elapsed time

Reflecting a function

The process of multiplying a function by negative one

Domain

The set of values of 𝑥 used for the input of the function

minimum

The smallest data point

standard form of a quadratic

The sum of a quadratic term, a linear term, and a constant in the form of𝑦=𝑎𝑥2 +𝑏𝑥+𝑐

degree of a monomial

The sum of the exponents of all the variables of a monomial

output

The value of a function given a certain value for the known variable

postive slope

The value of the slope in a function is positive; when a function is increasing.

Compressing a function

When a function is multiplied by a coefficient greater than zero but less than 1

increasing interval

When reading a graph from left to right, as the 𝑥 values increase, the 𝑦 values increase

decreasing interval

When reading a graph from left to right, as the 𝑥 values increase, the 𝑦 values decrease

term

a constant variable or multiplicative combination of the two

Roots

a solution to an equation usually as a number an algebraic formula

interquartile range

is the middle 50% of the data set; includes the data points that lie between the first quartile the third one quartile; also known as IQR.

undefined slope

vertical line

negative slope

falls from left to right

zero slope

horizontal line

compound inequality

ontains at least two inequalities that are joined by either "and" or "or"

zeros

same as solutions roots and x intercept

assocative property

states the contents of the parentheses will change

Commutative Property

states the ordered fo the numbers can be changed without the answer

GCF

the greatest factor that divides two numbers

inequality

the relationship between two expressions that are not equal