Classification of Functions Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which type of correspondence does a function exhibit if each input is linked to exactly one output?

Non-correspondence

Many-to-one correspondence

One-to-many correspondence

One-to-one correspondence (correct)

What does a function machine represent regarding input and output variables?

Input is always greater than output

Input is the dependent variable

Output is the independent variable

Input is the independent variable (correct)

How is the tricycle fare represented for distances greater than 2 kilometers in a piecewise function?

F(d) = 10 + 8d + 2 for d > 2

F(d) = 10 + 8(d - 2) for d > 2 (correct)

F(d) = 10 + 8d for d > 2

F(d) = 10 for d > 2

Which of the following is NOT a requirement for a function to pass the vertical line test?

Each input must correspond to multiple outputs (B) Signup and view all the answers

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?

S(n) = 750n (A) Signup and view all the answers

What is the representation of the computer rental fee as a function of the number of hours spent on the computer?

R(t) = 15t (C) Signup and view all the answers

Which of the following correctly describes the vertical line test?

A vertical line drawn through a graph must intersect it at exactly one point for it to be a function. (A) Signup and view all the answers

Given the functions defined in sets A and B, which statement is true?

Function A has a one-to-one correspondence for every input. (B) Signup and view all the answers

In which representation can a function be illustrated?

Through words, tables, mappings, equations, and graphs. (A) Signup and view all the answers

Which of the following is NOT a characteristic of a function?

An input can correspond to multiple outputs. (C) Signup and view all the answers

What defines a piecewise function?

A function that is composed of different functions applied to different intervals. (A) Signup and view all the answers

If a function machine adds three to its input, what is the output if the input is 5?

8 (A) Signup and view all the answers

Which relation is not a function according to the definition provided?

C = {(1,0), (0, 1), (-1,0), (0,-1)} (A) Signup and view all the answers

Why are relations like D considered not functions?

They have multiple outputs for one input. (B) Signup and view all the answers

What does it mean for a relation to be a function?

Each element in the domain has exactly one corresponding element in the range. (B) Signup and view all the answers

Which of the following relations is NOT a function?

C = {(1,0), (0,1), (-1,0), (0,-1)} (A), D = {(a,b), (b,c), (c,d), (a,d)} (B) Signup and view all the answers

How can the Vertical Line Test be used to determine if a graph represents a function?

If a vertical line intersects the graph more than once, it is not a function. (A), If a vertical line intersects the graph only once, it is a function. (C) Signup and view all the answers

What is true about one-to-one functions?

Each input in the domain must correspond to a unique output in the range. (A) Signup and view all the answers

Which of the following best describes a piecewise function?

A function defined by different expressions based on the input value. (B) Signup and view all the answers

What does evaluating a function involve?

Substituting a specific value into the function to find the corresponding output. (D) Signup and view all the answers

In the context of functions, what does the term 'domain' refer to?

The specific set of inputs for which the function is defined. (B), The set of all first elements in the ordered pairs. (C) Signup and view all the answers

What is represented by the set of ordered pairs in a function?

The correlation between input values (domain) and their corresponding outputs (range). (A) Signup and view all the answers

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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

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.