Function Vocabulary - Math II

Coordinate

A pair of numbers (x,y) that represents a point in a coordinate plane, as well as a solution that satisfies BOTH variables of a two-variable equation.

Function

A relation in which each input value (x) is paired with exactly one output value (f(x))

Continuous

A relation that includes all values within a certain range, including all fractional numbers. (Example: Filling a tank of gas)

Discrete

A relation that is not continuous, and so does not include some values. (Example: number of people in your class. We don't include partial people in that model).

Linear

A relationship between x and y values in which the outputs (y) add or subtract the same constant difference, x number of times

Quadratic

A relationship between x and y values in which the rate of change is linear (constant second difference means a constant acceleration)

Exponential

A relationship between x and y values where the total y is scaled or multiplied x number of times.

Domain

A set of all the input values ( x values )

Range

A set of all the output values ( f(x) values )

Binomial

A variable expression with two terms.

Multiple Representations

Descriptions, mapping diagrams, tables, graphs and equations.

First Difference

The differences between consecutive output values in a function table

Second Difference

The differences between consecutive values in the first difference in a function table.

Maximum

The greatest f(x) value in function. Always represented by the y value of the vertex of an inverted parabola.

Interval

The horizontal space between x values on a graph. For example, the horizontal space between the input values of 3 through 10, including 3 and 10, is written like this: [3, 10]

Minimum

The smallest f(x) value in a function. Always represented by the y value of the vertex of a parabola (the graph of a quadratic function).

Rate of Change

The speed at which the output changes over a specific change in x

f(3)

The value of a function at x=3. Or the output with an input of 3.

f(x)

The value of a function, given any input value. This variable is used as part of a description of a general pattern or relationship between all the input values and their respective output values. For example, f(x) = 2x means that the output is always twice the input, for any number you try.

Increasing Interval

The value of the function goes up in the given interval.

Input Variable

The x of an equation. The information put in to find the output.

Output Variable

The y or f(x) of an equation. The information gained after the input is plugged into an equation.

Variable

a symbol that represents an amount that can vary

Constant

a term that does not have a variable, and so does not change as x changes.