Relations and Functions
Function
A function is a relation in which each element of the domain corresponds with exactly one element in the range.
discrete graph
A graph composed of isolated points.
continuous graph
A graph is continuous if it has no jumps, breaks, or holes.
Interval notation
A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval.
set-builder notation
A notation used to describe the elements of a set.
one-to-one
A one-to-one function is a function for which each y-value in the range corresponds to exactly one x-value in the domain. A one-to-one function f has an inverse 𝘧−𝟣 that is also a function.
average rate of change
The average rate of change of the function over the interval 𝘢≤𝘹≤𝘣 is equal to 𝘧(𝘣)−𝘧(𝘢)𝘣−𝘢 .
domain
The domain of a relation is the set of all inputs, or x-coordinates, of the ordered pairs.
zero of a function
A zero of a function 𝘧(𝘹) is any value of x for which 𝘧(𝘹)=𝟢 .
relation
Any set of ordered pairs.
maximum
The maximum of a function is the greatest value that the function attains in its domain. It is the y -coordinate of the highest point on the graph of the function.
minimum
The minimum of a function is the least value that the function attains in its domain. It is the y-coordinate of the lowest point on the graph of the function.
range
The range of a relation is the set of all outputs or y-coordinates of the ordered pairs.