Questions and Answers
Which type of correspondence does a function exhibit if each input is linked to exactly one output?
What does a function machine represent regarding input and output variables?
How is the tricycle fare represented for distances greater than 2 kilometers in a piecewise function?
Which of the following is NOT a requirement for a function to pass the vertical line test?
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If a person earns ₱750.00 per day, how can total salary S be expressed as a function of the number n of days worked?
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What is the representation of the computer rental fee as a function of the number of hours spent on the computer?
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Which of the following correctly describes the vertical line test?
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Given the functions defined in sets A and B, which statement is true?
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In which representation can a function be illustrated?
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Which of the following is NOT a characteristic of a function?
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What defines a piecewise function?
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If a function machine adds three to its input, what is the output if the input is 5?
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Which relation is not a function according to the definition provided?
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Why are relations like D considered not functions?
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What does it mean for a relation to be a function?
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Which of the following relations is NOT a function?
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How can the Vertical Line Test be used to determine if a graph represents a function?
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What is true about one-to-one functions?
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Which of the following best describes a piecewise function?
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What does evaluating a function involve?
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In the context of functions, what does the term 'domain' refer to?
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What is represented by the set of ordered pairs in a function?
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Study Notes
Classification of Functions
- Functions can be classified into three types: one-to-one correspondence, one-to-many correspondence, and many-to-one correspondence.
- In a function machine, the input represents the independent variable while the output is the dependent variable.
Real-Life Function Representations
- Total salary (S) for a person earning ₱750.00 per day can be expressed as:
S(n) = 750n, where n is the number of days worked. - Rental fee (R) for a computer shop charging ₱15.00 per hour can be represented as:
R(t) = 15t, where t is the number of hours rented. - For a tricycle ride, the fare (F) can be expressed as a piecewise function:
F(d) = { 10, if d ≤ 2
10 + 8(d - 2), if d > 2 }
Here, d represents the distance in kilometers.
Evaluating Functions
- Functions can be evaluated by substituting the variable with specific values from the domain.
- Example evaluation: Determine Kevin's savings for a specific number of days.
Understanding Relations and Functions
- A relation is a set of ordered pairs, and the domain consists of the first elements while the range consists of the second elements.
- For a relation to be classified as a function, each domain element must correspond to exactly one range element.
- Examples of ordered pairs:
- Relation A = {(1,2), (2,3), (3,4), (4,5)} is a function.
- Relation B = {(3,3), (4,4), (5,5), (6,6)} is also a function.
- Relation C = {(1,0), (0,1), (-1,0), (0,-1)} is not a function because 0 corresponds to two different outputs.
- Relation D = {(a,b), (b,c), (c,d), (a,d)} is not a function due to repeated elements in the domain.
Graphical Representation and the Vertical Line Test
- A function can be illustrated using graphs in the Cartesian plane.
- The vertical line test states that a graph represents a function if any vertical line intersects it at exactly one point.
- Graph Examples:
- Graphs A and C pass the vertical line test, indicating they are functions.
- Graphs B and D fail the vertical line test, hence are not functions.
Multiple Representations of Functions
- Functions can be represented through various mediums: words, tables, mappings, equations, and graphs.
- Mathematical functions express a relationship where the output (y) depends on the input (x). For example, a function that adds three to the input can be denoted as y = x + 3.
Various Function Activities and Evaluations
- Activities include evaluating algebraic expressions and understanding real-life scenarios as functions.
- It is essential to practice evaluating functions and recognizing their applications in everyday situations.
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Description
Test your understanding of different types of functions and their representations in real-life scenarios. This quiz covers one-to-one, one-to-many, and many-to-one correspondences along with examples of salary and rental fees. Evaluate functions using provided formulas and piecewise functions.