Akshay_Anti said:That means that the domain or the value the variable can take is defined from that set. Eg- If I define a set over [a,b], it means the variable involved can take its value from a to b both inclusive only. For any other number out of this set, the function does not exist.
Intervals in respect to functions refer to the range of values that a function can take on. They are represented by a set of real numbers on a number line and can be open (excludes the endpoints) or closed (includes the endpoints).
Intervals are defined by the domain of a function, which is the set of all possible input values. The output values of the function within this domain make up the interval.
Understanding intervals in functions is crucial in determining the behavior and characteristics of a function. It helps in identifying the points of intersection, maximum and minimum values, and the overall shape of the function.
Yes, intervals can be infinite. This means that they have no specific starting or ending point and can continue indefinitely in one or both directions on the number line. For example, the interval (0,∞) represents all positive numbers greater than 0.
The intervals of a function determine the range of the graph and can affect its shape and direction. Open intervals result in a graph with dashed endpoints, while closed intervals have solid endpoints. The intervals also determine the smoothness or discontinuity of the graph.