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Detailed Video: Basics of Relations & Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Detailed Video: Basics of Relations & Functions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is a relation in mathematics? |  |
Ans. A relation in mathematics is a set of ordered pairs where the first element is related to the second element. It establishes a connection or association between two sets of objects, such as numbers or elements from different sets.
| 2. What is a function in mathematics? | |
Ans. In mathematics, a function is a special type of relation where each element in the domain is associated with exactly one element in the codomain. It means that for every input, there is a unique output. Functions are often represented by equations or graphs.
| 3. How can we determine if a relation is a function? | |
Ans. To determine if a relation is a function, we can use the vertical line test. If any vertical line intersects the graph of the relation at more than one point, then it is not a function. In other words, each input (x-value) should have a unique output (y-value) in a function.
| 4. What are the different types of functions? | |
Ans. There are several types of functions in mathematics, including:
- Linear functions: Functions with a constant rate of change, graphed as straight lines.
- Quadratic functions: Functions with a degree of 2, graphed as parabolas.
- Exponential functions: Functions where the variable appears as the exponent, often resulting in exponential growth or decay.
- Trigonometric functions: Functions involving angles, such as sine, cosine, and tangent.
- Logarithmic functions: Functions that are the inverse of exponential functions, often used to solve equations involving exponents.
| 5. How are relations and functions used in real-life situations? | |
Ans. Relations and functions are widely used in various real-life situations. For example:
- In economics, functions can be used to model supply and demand curves or calculate profit and cost functions.
- In physics, relations can represent the relationship between distance and time or the force applied to an object and its resulting acceleration.
- In computer science, relations and functions are essential for data analysis, algorithms, and programming.
- In biology, functions can model population growth or the relationship between genes and traits.
- In social sciences, relations can be used to analyze social networks or study the correlation between variables in surveys and experiments.
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