Questions and Answers
What is the mapping diagram for the relation ((-2,-6), (0,3), (1,-5), (5,0))?
-2 -> -6, 0 -> 3, 1 -> -5, 5 -> 0
What is the domain and range of the relation (-1, 1/2), (-1/2, -1), (3/2, 0), (2, 3/2)?
domain: (-1, -1/2, 3/2, 2); range: (-1, 0, 1/2, 3/2)
Is the relation {(14, 15), (5, 7), (3, 10), (11, 1), (5, 8)} a function?
False
Use the vertical line test to determine which graph represents a function.
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For f(x) = 5x + 1, what is f(-4)?
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What function rule models the cost of concert tickets that are $25 each with a $1.75 handling fee? Evaluate the function for 6 tickets.
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Study Notes
Mapping Diagrams and Functions
- A mapping diagram visually represents relationships by showing how each input corresponds to an output.
- Example relation:
- (-2 maps to -6)
- (0 maps to 3)
- (1 maps to -5)
- (5 maps to 0)
Graphing Relations
- Graph points:
- (-1, 1/2),
- (-1/2, -1),
- (3/2, 0),
- (2, 3/2)
- Domain consists of all x-values:
- (-1, -1/2, 3/2, 2)
- Range consists of all y-values:
- (-1, 0, 1/2, 3/2)
Identifying Functions
- A relation is not a function if an input is associated with multiple outputs.
- Example relation:
- {(14, 15), (5, 7), (3, 10), (11, 1), (5, 8)} is not a function because the input 5 corresponds to two outputs (7 and 8).
Vertical Line Test
- A graph represents a function if any vertical line drawn intersects it at most once.
- Identifying which graph passes this test is crucial for determining functions.
Function Evaluation
- Evaluate linear functions by substituting values into the function:
- For f(x) = 5x + 1, substituting x = -4 yields f(-4) = -19.
Cost Functions
- Functions can model real-world scenarios, like ticket pricing.
- Example function for concert tickets includes a base price and a handling fee:
- Total cost = 25t + 1.75
- For 6 tickets, evaluate function: Total cost = $151.75.
Studying That Suits You
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Description
Test your understanding of functions and relations with these flashcards designed for Algebra 2. Each card presents a different problem related to mapping diagrams, graphs, and identifying functions. Prepare to enhance your algebra skills through engaging practice!