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Relations and Functions Examples (NCERT) (Part -3) Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Relations and Functions Examples (NCERT) (Part -3) Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the difference between a relation and a function?
Ans. A relation is a set of ordered pairs, where the first element is related to the second element. On the other hand, a function is a special type of relation where each element from the first set (domain) is related to exactly one element in the second set (range). In other words, a function is a relation that satisfies the condition of having a unique output for every input.
2. Can a relation be both a function and a non-function at the same time?
Ans. No, a relation cannot be both a function and a non-function simultaneously. If a relation satisfies the condition of having a unique output for every input, it is a function. However, if there exists at least one input with multiple outputs, the relation is not a function.
3. How can we determine if a relation is a function or not?
Ans. To determine whether a relation is a function or not, we need to check if each element from the first set (domain) is related to exactly one element in the second set (range). If there is any element in the domain that has multiple outputs in the range, then the relation is not a function.
4. What are the different types of functions?
Ans. There are different types of functions based on their properties. Some common types of functions include: - One-to-one function: A function where each element in the domain is related to a unique element in the range. - Onto function: A function where every element in the range has at least one corresponding element in the domain. - Many-to-one function: A function where multiple elements in the domain are related to the same element in the range. - Constant function: A function where the output is the same for every input. - Identity function: A function where the output is equal to the input.
5. How can we represent a function using an equation or a graph?
Ans. A function can be represented using an equation or a graph. - Equation representation: In an equation, we usually use the variable "x" to represent the input (domain) and "y" to represent the output (range). The equation expresses the relationship between the input and output. For example, a linear function can be represented as y = mx + b, where "m" is the slope and "b" is the y-intercept. - Graph representation: In a graph, the input (domain) is represented on the x-axis, and the output (range) is represented on the y-axis. The points on the graph represent the ordered pairs of the function. The shape and position of the graph convey the relationship between the input and output. For example, a linear function will have a straight line on the graph.
204 videos|288 docs|139 tests

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