31 terms

Compare and Contrast Functions key terms

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arithmetic sequence
a sequence of numbers in which the difference between any consecutive terms is the same
average rate of change
the change in the value of a quantity by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph.
coefficient
a number multiplied by a variable in an algebraic expression
constant rate of change
with respect to the variable x of a linear function y = f(x), the _______ _______ _______ _______ is the slope of its graph.
continuous
describes a connected set of numbers, such as an interval
discrete
a set with elements that are disconnected
domain
the set of x-ccordinates of the set of points on a graph
the set of x-coordinates of a given set of ordered pairs
the value that is the input in a function or relation
end behaviors
the appearance of a graph as it is followed farther and farther in either direction
explicit expression
a formula that allows direct computation of any term for a sequence a_1, a_2, a_3, ... a_n, ...
exponential function
a nonlinear function in which the independent value is an exponent in the function, as in y = a(b^x)
exponential model
an exponential function representing real-world phenomena. The _______ also represents patterns found in graphs and/or data.
expression
any mathematical calculation or formula combining numbers and/or variables using sums, differences, products, quotients including fractions, exponents, roots, logarithms, functions, or other mathematical operations
even function
a function with a graph that is symmetric with respect to the y-axis. A function is only a(n) _______ _______ iff f(-x) = f(x).
factor
For any number x, the numbers that can be evenly divided into x are called _______s of x. For example, the number 20 has the _______s 1, 2, 4, 5, 10, and 20.
geometric sequence
a sequence of numbers in which the ratio between any two consecutive terms is the same. In other words, you multiply by the same number each time to get the next term in the sequence. This fixed number is called the common ratio for the sequence.
horizontal shift
a rigid transformation of a graph in a horizontal direction, either left or right
interval notation
a notation representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parenthese and/or brakcets are used to show whether the endpoints are excluded or included.
linear function
a function with a constant rate of change and a straight line graph
linear model
a linear function representing greal-world phenomena. The _______ also represents patterns found in graphs and/or data.
odd function
a function with a graph that is symmetric with respect to the origin. A function is a(n) _______ _______ iff f(-x) = - f(x).
parameter
the independent variable or variables in a system of equations with more than one dependent variable
quadratic equation
a equation of degree 2, which has at most two solutions.
quadratic function
a function of degree 2 which has a graph that "turns around" once, resembling an umbrella-like curve that faces either right-side up or upside down. This graph is called a parabola.
root
the x-value where the function has a value of zero
range
the set of y-coordinates of the set of points on a graph
the set of y-coordinates of a given set of ordered pairs
the set of all possible outputs of a function or relation
recursive formula
a formula that requires the computation of all previous terms to find the value of a_n
slope
the ratio of the vertical and horizontal changes between two points on a surface or a line
term
a value in a sequence- the first value in a sequence is the first _______, the second value is the 2nd _______, and so on. A _______ is also any of the monomials that make up a polynomial.
vertical translation
a shift in which a plane figure moves vertically
x-intercept
the point where a line meets or crosses the x-axis
y-intercept
the point where a line meets or crosses the y-axis