What really are intervals in respect to functions ? As defined they

In summary, intervals in respect to functions are subsets of real numbers, denoted by two numbers a and b belonging to R, with a<b. These intervals can be inclusive or exclusive and can also be infinite. The variables a and b define the domain or the values that the variable can take in the function. For example, if a set is defined over [a,b], the variable can only take values from a to b, and any other value outside of this set will result in a non-existent function.
  • #1
Kartik.
55
1
What really are intervals in respect to functions ? As defined they are subsets of real numbers, for example, two numbers a,b belonging to R and a<b, so with that we can make out four intervals or sets with some variable x and treating a and b are inclusive or exclusive limits and also some infinite intervals :\. How does that have any utility with functions and what are these variables a and b for ? Please someone elaborate on this ?
 
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  • #2


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.
 
  • #3


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.

Thanks You .
 

FAQ: What really are intervals in respect to functions ? As defined they

1. What are intervals in respect to functions?

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).

2. How are intervals defined for functions?

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.

3. What is the purpose of understanding intervals in functions?

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.

4. Can intervals be infinite?

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.

5. How do intervals affect the graph of a function?

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.

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