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Algebra Midterm Vocabulary-set 1
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Terms in this set (57)
Coefficient
The numerical factor of a term
Constant
A real number
Common difference
found by subtracting 2 successive terms in an arithmetic sequence
Continuous Graph
A graph made up of connected points(linear or non-linear)
Arithmetic Sequence
A sequence which each term is found by adding the same Integer to the previous term
Natural Numbers
The set of the numbers: 1,2,3,4....
Whole Numbers
The set of numbers: 0,1,2,3,4....
Integers
The set of numbers: ...-3,-2,-1,0,1,2,3...
The whole numbers and their opposites
Rational Numbers
The set of numbers that can be written as fractions a/b where a and b are integers and b does not equal 0. This includes terminating and repeating decimals.
Irrational Numbers
Numbers that cannot be written in fraction form a/b where a and b are integers and b does not equal 0.
Real Numbers
The set of rational and irrational numbers.
Slope
The ratio of horizontal change to vertical change. Rise/Run
x-intercept
x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero
y-intercept
The point where the graph crosses the y-axis. What the y coordinate is when the x coordinate is zero.
Range
The y-coordinates of the set of points on a graph or in ordered pairs. The range is the output in a function or a relation.
Domain
The set of x-coordinates of the set of points on a graph or in ordered pairs. The value that is the input in a function or relation.
Negative correlation
the relationship between two variables in which one variable increases as the other variable decreases
Positive correlation
A correlation where as one variable increases, the other also increases, or as one decreases so does the other. Both variables move in the same direction.
No correlation
there does not appear to be a relationship between two sets of data
Function
a relation where each number in the domain is paired with exactly one number in the range.
Discrete graph
a graph made up of unconnected points
Rate or Rate of Change
A ratio of two quantities measured in different units.
Examples:change over time, mph, beats per minute
Linear equation or function
an equation or function which contains a variable which is not raised to any power other than 1 and whose graph is a straight line.
Slope intercept form
an equation written in the form y=mx+b is in slope-intercept form. The graph is a line with slope m and y-intercept b.
Absolute value
The distance a number is from zero on a number line
Relation
a mapping, or pairing, of input values with output values or a set of ordered pairs
Simplify
combining like terms
To make a fraction easier to work with by taking out common factors. In an expression, combining variables that have like unknowns.
Inverse
A value that brings a number back to the identity (o or 1) under a given operation.
Standard Form
Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
Point Slope Form
y-y₁=m(x-x₁), where m is the slope and (x₁,y₁) is the point the line is passing through.
Term
a number or a variable or the product of a number and a variable , also what each number in a sequence is named
constant of variation
what the k is in the equation y = kx
direct variation
Increase (or decrease) in one variable causes a proportional increase (or decrease) in another variable (y=kx)
zero of a function
An x-intercept of the graph of a function.For the function f, any number x such that f(x) = 0
root of an equation
Any value that makes the equation true or
a solution of an equation
independent variable
The input or domain
dependent variable
The output or the range
Vertical Line Test
If any vertical line passes through more than one point of the graph, the relation is not a function.
Reflexive Property
--Real Numbers--For any real number a, a=a
Symmetric Property
For all numbers a & b, if a = b, then b = a.(ex. the segment GH = segment HG)
Transitive Property
--Real Numbers-- For any real numbers a, b, and c,if a=b and b=c, then a=c
Substitution Property
For all numbers a & b, if a = b, then a may be replaced by b in any equation or expression.
Multiplicative Identity
For any real number a, a
1 =a and 1
a = a.
Multiplicative Inverse
A fraction times its reciprocal equals 1. (Neither the numerator or the denominator can be 0)
Additive Identity
a+0=a, the sum of any real number & zero is a equal to the number.
Additive Inverse
The additive inverse of any real number x is the number that gives zero when added to x. The additive inverse of 5 is -5.
Distributive Property
For all numbers a,b & c, a(b + c) = ab + ac
Commutative Property
A property that states that two or more numbers can be added/ multiplied in any order without changing the sum/product
Associative Propety
When you have an addition or multiplication problem that has parenthese you can move the parenthese around and still get the same result.
Proportional relationship
a relationship between variables in a problem that is characterized by three things: 1) there is a constant rate of change between the variables- y/x is constant for any ordered pair, 2) the graph goes through the origin, and 3) the equation for the function has the form y = kx where k is the constant of proportionality, y/x - A direct variation
Best Fit Line
a straight line on a scatterplot that best represents the data; it may or may not pass through some or all of the data points
scatter plot
A graph that displays two sets of data as ordered pairs (points)
Parallel Lines
Lines in the same plane that have the same slope or are vertical lines.
Perpendicular lines
Lines that intersect to form right angles whose slope are the opposite reciprocal of each other
Bivariate Data
Data with two variables written as ordered pairs
Linear Interpolation
the use of a linear equation to predict values that are inside of the range of data by substitution or reading it's graph
Inverse relation
A set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair.
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