Algebra 1 Test Questions: Functions from Mapping Diagrams.

📚 Quick Study Guide

• 📌 Definition of a Function: A function is a relation where each input (x-value) has exactly one output (y-value). Think of it as a machine: you put something in, and you only get one specific thing out.
• 🗺️ Mapping Diagrams: These diagrams visually show how inputs are mapped to outputs. The inputs are usually listed on the left, and the outputs on the right, with arrows connecting them.
• ✅ Function Test (Mapping Diagrams): To determine if a mapping diagram represents a function, check if any input value has more than one arrow coming out of it. If an input has multiple arrows, it's NOT a function. If each input has only one arrow, it IS a function.
• 📝 Domain and Range:
  • 🎯 Domain: The set of all possible input values (x-values).
  • 📈 Range: The set of all possible output values (y-values).
• 🧮 Representing Functions: Functions can be represented in many ways, including mapping diagrams, graphs, equations, and tables.
• 💡 Notation: $f(x)$ represents the output of the function $f$ when the input is $x$. For example, if $f(x) = x + 2$, then $f(3) = 3 + 2 = 5$.

Practice Quiz

1. Which of the following mapping diagrams represents a function?
   1. Each input has exactly one output
   2. At least one input has two or more outputs
   3. No inputs have any outputs
   4. All outputs are the same
2. Consider a mapping diagram where the input 2 maps to both 4 and 5. Does this diagram represent a function?
   1. Yes
   2. No
   3. Cannot be determined
   4. Only if the outputs are positive
3. In a mapping diagram, if every input has only one arrow pointing to an output, the diagram is best described as:
   1. A non-function
   2. A function
   3. A relation, but not necessarily a function
   4. An undefined relation
4. What is the domain of the function represented by the mapping diagram where inputs are {1, 2, 3} and outputs are {4, 5, 6}?
   1. {4, 5, 6}
   2. {1, 2, 3, 4, 5, 6}
   3. {1, 2, 3}
   4. { } (empty set)
5. What is the range of the function represented by a mapping diagram with inputs {a, b} mapping to outputs {7, 8, 9}, where 'a' maps to 7 and 'b' maps to 8?
   1. {a, b}
   2. {7, 8, 9}
   3. {7, 8}
   4. {9}
6. If a mapping diagram shows input -1 mapping to output 2, input 0 mapping to output 2, and input 1 mapping to output 2, does this represent a function?
   1. Yes
   2. No
   3. Only if the inputs are positive
   4. Cannot be determined
7. Which statement is TRUE about mapping diagrams representing functions?
   1. An input can map to many outputs
   2. An output can map to many inputs
   3. Inputs must always be positive
   4. There must be more inputs than outputs