Key Terms
Meaning
Example
U6 L1
What does it mean to be a Function?
Function:
Relation:
U6 L2
Independent variable/
Dependent variable
Independent variable:
Dependent variable:
U6 L2
Function notation
U6 L2
Ordered Pair (x, y)
U6 L2
Vertical Line Test
U6 L2
Linear/
NonLinear function
Linear:
NonLinear:
How to tell from a table:
How to tell from a graph:
How to tell from an equation:
U6 L1:
Function: A function is a relation where each input (x-value) has exactly one output (y-value). It can also be described as a rule or an equation that assigns each input with a unique output.
Relation: A relation is a set of ordered pairs. It describes the relationship between two sets of values or variables.
Example: A function can be represented by the equation y = 2x + 3, where for every input value of x, there is a unique output value of y.
U6 L2:
Independent variable: The independent variable is the variable that is input or controlled by the person or experiment. It is also known as the "x-variable" in a function.
Dependent variable: The dependent variable is the variable that is output or dependent on the independent variable. It is also known as the "y-variable" in a function.
Function notation: Function notation is a way of representing a function using symbols. It is typically written as f(x), where f represents the function and x represents the input value.
Ordered Pair (x, y): An ordered pair is a pair of numbers in a specific order. In the context of functions, an ordered pair represents a pair of values where the first value is the input (x-value) and the second value is the output (y-value).
Vertical Line Test: The vertical line test is a test used to determine whether a graph represents a function. If a vertical line can intersect the graph at more than one point, then the graph does not represent a function.
Linear: A linear function is a function that has a constant rate of change, meaning that the change in the output value is directly proportional to the change in the input value. It can be represented by a straight line on a graph.
Nonlinear: A nonlinear function is a function that does not have a constant rate of change. The change in the output value is not directly proportional to the change in the input value. It cannot be represented by a straight line on a graph.
How to tell from a table: In a table, if the change in the output (y-value) is constant for each change in the input (x-value), then the function is linear. If the change in the output is not constant, then the function is nonlinear.
How to tell from a graph: On a graph, if the points form a straight line, the function is linear. If the points do not form a straight line, the function is nonlinear.
How to tell from an equation: In an equation, if the highest exponent of the variable is 1, the function is linear. If the highest exponent is greater than 1 or if there are terms with variables multiplied together or raised to a power, the function is nonlinear.