functions Vocabulary
JamWise Education Team·Updated March 2026
The functions strand is a core part of the K-8 math curriculum. It encompasses 18 vocabulary terms that students encounter as they progress from kindergarten through 8th grade. Each term builds on previous knowledge, creating a spiral of deepening understanding that prepares learners for increasingly complex concepts.
Understanding functions vocabulary is essential for classroom discussions, assessments, and real-world application. Below you will find every term organized by grade level, so teachers and parents can quickly identify which words are appropriate for their students and explore definitions tailored to each developmental stage.
8th Grade
(18 terms)
Decreasing function
A function whose output gets smaller as the input gets larger. Its graph goes down from left to right.
Domain
The set of all possible input values for a function. For example, if f(x) = √x, the domain is all non-negative numbers.
Function
A rule that assigns exactly one output to each input. If you put in an input value, you always get the same output. Written as f(x).
Function notation
A way to write functions using the format f(x), where f names the function and x is the input. f(3) means the output when the input is 3.
Graph of a function
The set of all points (x, f(x)) plotted on a coordinate plane. Each input x maps to one output f(x).
Increasing function
A function whose output gets larger as the input gets larger. Its graph goes up from left to right.
Initial value
The output of a function when the input is zero. In y = mx + b, the initial value is b. On a graph, it is the y-intercept.
Input
The value you put into a function. Also called the independent variable or x-value. In f(3), the input is 3.
Linear function
A function whose graph is a straight line. It can be written as f(x) = mx + b, where m is the slope and b is the y-intercept.
Nonlinear function
A function whose graph is not a straight line. The rate of change is not constant. Quadratic and exponential functions are nonlinear.
Ordered pair
A pair of numbers (x, y) that gives the position of a point on a coordinate plane. The first number is the x-coordinate and the second is the y-coordinate.
Output
The value a function produces for a given input. Also called the dependent variable or y-value. If f(x) = 2x + 1, the output for input 3 is 7.
Qualitative graph
A graph that shows the general shape of a relationship without exact numbers. It describes patterns like increasing, decreasing, or staying constant.
Range
The set of all possible output values of a function. It depends on the domain and the function rule.
Rate of change
How quickly one quantity changes compared to another. For a linear function, the rate of change is constant and equals the slope.
Table of values
A table showing input-output pairs for a function. Each row has an x-value and its corresponding y-value.
Vertical line test
A test to determine if a graph represents a function. If any vertical line touches the graph at more than one point, it is not a function.
X-intercept
The point where a graph crosses the x-axis. At this point, the y-value is zero.