Algebra 1 Unit 2 Vocabulary
direct variation
A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. y = kx or k=y/x If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).
arithmetic sequence
A sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, -3, -8, -13, -18 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n.
parent function
A set of basic functions used as building blocks for more complicated functions. The list of parent functions varies. The most basic function of a particular category or type.
relation
A set of ordered pairs. For example, {(1, 2), (3, 4), (1, a), (5, r)} is a relation. So is the set {(x, y): y = x2}; this is the set of all ordered pairs (x, y) for which y = x2.
descrete
A set with elements that are disconnected. The set of integers is discrete. The set of real numbers is not discrete; it is continuous. Formally, a set of numbers is discrete if each number in the set is contained in a neighborhood that contains no other elements of the set.
x-intercept
A point at which a graph intersects the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros.
y-intercept
A point at which a graph intersects the y-axis.
z-intercept
A point at which a graph intersects the z-axis.
function
A relation for which each element of the domain corresponds to exactly one element of the range. For example, is a function because each number x in the domain has only one possible square root. On the other hand, is not a function because there are two possible values for any positive value of x.
correlation
The association, between two sets of data.
inverse function
f^-1(x) is read as "f inverse of x". It does not mean "f to the negative one power."
one-to-one
no two values of x are paired with the same value of y
negative correlation
where y tends to decrease as x increases
∆
delta, change
point-slope form
"y - y sub 1 = m(x - x sub 1)", where m is the slope and ("x sub 1, y sub 1") is a point on the line.
scatter plot
A graph of paired data in which the data values are plotted as (x, y) points. It displays the relationship between two sets of numerical data. It can reveal trends in data.
slope
A measure of the amount of decline or incline of a line represented by m.
vertical line test
A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.
independent variable
A variable in an equation that may have its value freely chosen without considering values of any other variable. For equations such as y = 3x - 2, the independent variable is x. The variable y is not independent since it depends on the number chosen for x. Formally, an independent variable is a variable which can be assigned any permissible value without any restriction imposed by any other variable.
dependent variable
A variable that depends on one or more other variables. For equations such as y = 3x - 2, the dependent variable is y. The value of y depends on the value chosen for x. Usually the dependent variable is isolated on one side of an equation. Formally, a dependent variable is a variable in an expression, equation, or function that has its value determined by the choice of value(s) of other variable(s).
explicit formula
An _______________ for an arithmetic sequence describes any term in the sequence using the first term and the common difference.
absolute value function
An absolute value function is written as f(x) = |x| and is defined by f(x)=−x if x<0 f(x) =x if x≥0
extrema
An extreme value of a function. In other words, the minima and maxima of a function. Extrema may be either relative (local) or absolute (global).
standard form
Ax + By = C, where A > 0 and, if possible, A, B, and C are relatively prime integers.
continuous
Describes a connected set of numbers, such as an interval. For example, the set of real numbers is continuous. The set of integers is not continuous; it is discrete.
relative maximum
The highest point in a particular section of a graph. (not the end points)
relative minimum
The lowest point in a particular section of a graph. (not the end points)
domain
The set of values of the independent variable(s) for which a function or relation is defined. Typically, this is the set of x-values
range
The set of y-values of a function or relation. More generally, the range is the set of values assumed by a function or relation over all permitted values of the independent variable(s).
no correlation
a lack of association or between x and y
trend line
a line drawn on a scatter plot to show the correlation
quadratic regression
a method used to find a quadratic function that models a set of data using a graphing calculator.
exponential regression
a method used to find an exponential function that models a set of data using a graphing calculator.
linear regression
a method used to find the line of best fit - we will be using a graphing calculator or graphing program
exponential function
a nonlinear function that can be written in the form y = ab^x. You will study exponential functions in more detail later in this book.
quadratic function
a nonlinear function that can be written in the form y = ax 2 + bx + c, where a ≠ 0.
indirect variation
also known as inverse variation. y=k/x
linear equation
an equation that can be written in standard form Ax + By = C where A, B, and C are constants and A and B cannot both be zero.
line of best fit
can be created using a graphing calculator, a spreadsheet program, or other Computer Algebra Systems (CAS).
constant of a variation
in Direct variation where y = kx, where k ≠ 0 and the coefficient k is this
quadratic function
y = ax^ 2 + bx + c, where a ≠ 0.
slope-intercept form
y = mx + b, where m is the slope and b is the y-intercept.
positive correlation
y tends to increase as x increases.