1.What is a Function?2.What is relation in Mathematics?3.What are the Five ways in representing a relation. give example of each 4.What is domain?5.What is a renge?6.What are the three Classification of a corresponding give illustrative example for each.
Answer (1)
Answer:Here's a breakdown of the concepts you've asked about, along with examples:**1. What is a Function?**A function is a special type of relation where each input (x-value) has exactly one output (y-value). Think of it like a machine: you put something in, and it always gives you a specific, predictable result.**Example:** The function f(x) = x + 2 takes any number you input (x) and adds 2 to it. So:* f(1) = 1 + 2 = 3* f(5) = 5 + 2 = 7* f(-2) = -2 + 2 = 0**2. What is a Relation in Mathematics?**A relation is a set of ordered pairs (x, y) that shows a connection between two sets of values. It doesn't have the same strict "one input, one output" rule as a function.**Example:** The relation "is taller than" could be represented by pairs like (John, Mary) if John is taller than Mary. This relation doesn't have to be unique – John could be taller than several people.**3. Five Ways to Represent a Relation:**1. **Set of Ordered Pairs:** {(1, 2), (3, 4), (5, 6)}2. **Mapping Diagram:** A visual representation with arrows connecting inputs to outputs.3. **Table:** A table with columns for inputs (x) and outputs (y).4. **Graph:** A plot of points on a coordinate plane.5. **Equation:** A mathematical equation that defines the relationship between x and y.**Example:** Let's use the relation "y is twice x"* **Set of Ordered Pairs:** {(1, 2), (2, 4), (3, 6), ...}* **Mapping Diagram:** Draw arrows from 1 to 2, 2 to 4, 3 to 6, etc.* **Table:** | x | y | |---|---| | 1 | 2 | | 2 | 4 | | 3 | 6 |* **Graph:** Plot the points (1, 2), (2, 4), (3, 6), etc. on a coordinate plane.* **Equation:** y = 2x**4. What is Domain?**The domain of a relation or function is the set of all possible input values (x-values).**Example:** In the function f(x) = x + 2, the domain is all real numbers because you can input any number.**5. What is Range?**The range of a relation or function is the set of all possible output values (y-values).**Example:** In the function f(x) = x + 2, the range is also all real numbers because you can get any number as an output by choosing the right input.**6. Classification of Relations:**1. **One-to-One:** Each input has exactly one unique output. * **Example:** f(x) = x (The function simply returns the input)2. **Many-to-One:** Multiple inputs can have the same output. * **Example:** f(x) = x² (Both 2 and -2 have an output of 4)3. **One-to-Many:** One input can have multiple outputs. * **Example:** This is not a function! A function cannot have multiple outputs for a single input.Let me know if you'd like more examples or have any other questions!
