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Relations and Functions | CBSE Class 12 Maths | Neha Agrawal Mam | Vedantu Math Video Lecture - JEE
FAQs on Relations and Functions - CBSE Class 12 Maths - Neha Agrawal Mam - Vedantu Math Video Lecture - JEE
| 1. What is the difference between relations and functions in mathematics? |  |
Ans. Relations and functions are both concepts in mathematics, but they have distinct characteristics. A relation is a set of ordered pairs, where each ordered pair consists of two elements from different sets. On the other hand, a function is a special type of relation in which each element of the first set is paired with exactly one element from the second set. In simpler terms, a function is a relation that assigns a unique output to each input.
| 2. How can we determine if a relation is a function or not? | |
Ans. To determine if a relation is a function or not, we use the concept of the vertical line test. If every vertical line intersects the graph of the relation at most once, then the relation is a function. This means that for each input value, there is only one corresponding output value. However, if a vertical line intersects the graph at more than one point, then the relation is not a function.
| 3. What is the domain and range of a function? | |
Ans. The domain of a function is the set of all possible input values or the independent variable. It represents the values for which the function is defined. The range of a function, on the other hand, is the set of all possible output values or the dependent variable. It represents the values that the function can take.
| 4. How can we determine the domain and range of a function from its graph? | |
Ans. To determine the domain and range of a function from its graph, we look at the x-axis for the domain and the y-axis for the range. The domain is the set of all x-values for which the graph is defined. It includes all the points on the x-axis that correspond to the graph. The range is the set of all y-values that the graph takes. It includes all the points on the y-axis that correspond to the graph.
| 5. Can a function have the same output for different input values? | |
Ans. No, a function cannot have the same output for different input values. According to the definition of a function, each input value should be paired with exactly one output value. This means that each input should have a unique output. If a function has the same output for different input values, it violates this rule and is not considered a function.
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