Comparing and Contrasting Functions Unit 5 Comparing and Contrasting Functions

A sequence of numbers in which the difference between any two consecutive terms is the same. Arithmetic Sequence

The change in the value of a quantity by the elapsed time 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. Average Rate of Change

A number multiplied by a variable in an algebraic expression. Coefficient.

Constant Rate of Change. With respect to the variable x of a linear function y = f(x), the constant rate of change is the slope of its graph. Constant Rate of Change.

Describes a connected set of numbers, such as an interval. Continuous.

A set with elements that are disconnected Discrete.

The set of x-coordinates 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 Domain

The appearance of a graph as it is followed farther and farther in either direction End Behaviors.

A formula that allows direct computation of any term for a sequence a1, a2, a3, . . . , an, . . . . Explicit Expression

A nonlinear function in which the independent value is an exponent in the function, as in y = abx. Exponential Function

An exponential function representing real-world phenomena An exponential function representing real-world phenomena. The model also represents patterns found in graphs and/or data. Exponential Model

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. Expression

A function with a graph that is symmetric with respect to the y- axis A function with a graph that is symmetric with respect to the y- axis. A function is only even if and only if f(–x) = f(x). Even Function.

For any number x, the numbers that can be evenly divided into x are called factors of x. For example, the number 20 has the factors 1, 2, 4, 5, 10, and 20 Factor

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. • Geometric Sequence.

A rigid transformation of a graph in a horizontal direction, either left or right Horizontal shift.

A notation representing an interval as a pair of numbers A notation representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included Interval Notation

A function with a constant rate of change and a straight line graph Linear Function

A linear function representing real-world phenomena A linear function representing real-world phenomena. The model also represents patterns found in graphs and/or data. Linear Model.

A function with a graph that is symmetric with respect to the origin A function with a graph that is symmetric with respect to the origin. A function is odd if and only if f(–x) = –f(x) Odd Function

The independent variable or variables in a system of equations with more than one dependent variable Parameter

An equation of degree 2, which has at most two solutions Quadratic equation

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 Quadratic function

The x–values where the function has a value of zero Root.

The set of all possible outputs of a function. Range.

A formula that requires the computation of all previous terms to find the value of a succeeding term. Recursive Formula.

The ratio of the vertical and horizontal changes between two points on a surface or a line • Slope.

A value in a sequence--the first value in a sequence is the 1st term, the second value is the 2nd term, and so on; a term is also any of the monomials that make up a polynomial Term.

A shift in which a plane figure moves vertically Vertical Translation.

The point where a line meets or crosses the x-axis X-intercept.

The point where a line meets or crosses the y-axis Y-intercept.