Mapping diagrams for functions and relations: Explained with examples.

📚 Quick Study Guide

• 🔢 A relation is a set of ordered pairs $(x, y)$.
• 📈 A function is a special type of relation where each input $x$ has only one output $y$.
• 📍 Mapping diagrams visually represent relations and functions using arrows to show the correspondence between elements.
• ➡️ In a mapping diagram for a function, each element in the domain has exactly one arrow emanating from it.
• 📝 Vertical Line Test: A visual test to determine if a graph represents a function. If any vertical line intersects the graph more than once, it's not a function.
• 🎯 Domain: The set of all possible input values ($x$-values).
• ✨ Range: The set of all possible output values ($y$-values).

🧪 Practice Quiz

1. Question 1: Which of the following mapping diagrams represents a function?
1. Each element in the domain maps to one or more elements in the range.
2. Some elements in the domain are not mapped to any element in the range.
3. Each element in the domain maps to exactly one element in the range.
4. Some elements in the range are not mapped to by any element in the domain.
2. Question 2: Consider the relation {(1, 2), (2, 4), (3, 6), (1, 8)}. Why is this relation NOT a function?
1. Because the $y$-values are all even numbers.
2. Because the $x$-values are increasing.
3. Because the $x$-value 1 maps to two different $y$-values (2 and 8).
4. Because the $y$-value 8 is the largest number.
3. Question 3: In a mapping diagram, what does an arrow represent?
1. A coordinate on a graph.
2. The relationship or mapping between an input and an output.
3. A variable in an equation.
4. The slope of a line.
4. Question 4: Which of the following sets of ordered pairs represents a function?
1. {(1, 2), (2, 3), (1, 4)}
2. {(1, 2), (2, 2), (3, 2)}
3. {(1, 2), (2, 3), (3, 2), (2, 1)}
4. {(1, 2), (1, 3), (1, 4)}
5. Question 5: What is the domain of the relation {(0, 1), (1, 2), (2, 3)}?
1. {1, 2, 3}
2. {0, 1, 2, 3}
3. {0, 1, 2}
4. { } (empty set)
6. Question 6: What is the range of the function $f(x) = x^2$ when the domain is {-2, -1, 0, 1, 2}?
1. {-4, -1, 0, 1, 4}
2. {0, 1, 4}
3. {0, 1, 2}
4. {0, 1, 2, 4}
7. Question 7: Which test is used to determine whether a graph represents a function?
1. Horizontal Line Test
2. Diagonal Line Test
3. Vertical Line Test
4. Curve Test