General Mathematics Quiz

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Questions and Answers

What is the product of the functions when given $f(x) = 3x - 4$ and $g(x) = x + 8$?

$3x^2 + 12x - 32$

$3x^2 + 24x - 32$ (correct)

$3x^2 + 24x - 4$

$3x^2 + 20x - 32$ (correct)

If $f(x) = 6x - 5$ and $g(x) = 4x + 2x + 9$, what is $(fg)(x)$?

$24x^2 - 24x + 30$

$24x^2 - 8x + 44$ (correct)

$24x^2 - 44x - 45$

$24x^2 - 8x + 45$

What is the value of $(fg)(-2)$ given $f(x) = 24x - 8$ and $g(x) = 44x - 45$?

$-457$

$-275$

$-100$

$-357$ (correct)

For the quotient $(f/g)(x)$ when $f(x) = x + 2$ and $g(x) = x - 5$, what is the result?

$\frac{x + 2}{x - 5}$ Signup and view all the answers

Given the functions $f(x) = 2x + 5$ and $g(x) = x - 24$, what is the resulting expression for the quotient $(f/g)(x)$?

$\frac{2x + 5}{x - 24}$ Signup and view all the answers

What is the distance covered if walking for 3 hours at a speed expressed by the function $f(x) = 7x$?

21 miles Signup and view all the answers

What is the height of the ball after 5 seconds if it is dropped from a 75m building using the function $h(t) = 5.8t + 72$?

217 m Signup and view all the answers

If the area of an equilateral triangle is given by the function $A(s)$, what is the area when the side measures 8 cm?

27.71 cm² Signup and view all the answers

Using the functions $f(x) = 3x - 3$ and $g(x) = 10x + 4$, what is the result of $(f + g)(x)$?

13x + 1 Signup and view all the answers

What is the difference $(f - g)(x)$ if given $f(x) = x - 1$ and $g(x) = 6x + 2x + 4$?

−6x − 5 Signup and view all the answers

Given the function $C(F)$ for Celsius temperature from Fahrenheit, what is the Celsius equivalent for a Fahrenheit temperature of 32°F?

0°C Signup and view all the answers

If $A$ represents the area of an equilateral triangle, what would the area be when the side length is 16 cm?

77.25 cm² Signup and view all the answers

What is the outcome of evaluating the sum of functions $(f + g)(5)$ if given $f(x) = 7x + 4x - 2x - 2$ and $g(x) = 2x + 3$?

63 Signup and view all the answers

What is the definition of a function?

A relation in which each element of the domain corresponds to exactly one element of the range. Signup and view all the answers

Which of the following statements correctly differentiates a function from a relation?

All functions are relations but not all relations are functions. Signup and view all the answers

What constitutes the domain of a relation?

The set of first coordinates. Signup and view all the answers

If a relation has the pairs (2, 4), (3, 4), and (2, 5), is it a function?

No, because the input 2 corresponds to two different outputs. Signup and view all the answers

Which characteristic is essential for a function?

Each element of the domain corresponds to at least one element of the range. Signup and view all the answers

Which of the following is an example of a relation but not a function?

{(1, 2), (1, 3), (2, 3)} Signup and view all the answers

How can one determine if a given relation is a function?

By using the vertical line test on its graph. Signup and view all the answers

Which of the following numbers is classified as a prime number?

11 Signup and view all the answers

What characteristic must a relation fulfill to be classified as a function?

Each element of X must be assigned to an element of Y. Signup and view all the answers

What does the vertical line test determine?

If a set of points in a coordinate plane is a function. Signup and view all the answers

Given the function $f(x) = 3x$, what is the value of $f(4)$?

12 Signup and view all the answers

If Aiah walks at a speed of 7 km/hr, how will her distance covered be represented as a function?

f(t) = 7t, where t is the time in hours. Signup and view all the answers

What can be inferred about the elements of Y in a function?

Some elements of Y may not correspond to any element of X. Signup and view all the answers

What is a mapping diagram used for?

To visually show the relationship between two sets. Signup and view all the answers

If a function is represented by the ordered pairs {(2,1), (7,4), (-3,1), (9,-4)}, which ordered pair indicates a repeated output?

(2, 1) Signup and view all the answers

Which of the following statements about relations and functions is true?

All functions are relations, but not all relations are functions. Signup and view all the answers

What is the result of evaluating $f(b) = b - 7$ when $b = -5$?

2 Signup and view all the answers

How much will Mikha earn in a month if her daily salary is represented by the function $f(x) = 585(x)$ and she works for 22 days?

12,870 Signup and view all the answers

Study Notes

Prayer and Introduction

Opening prayer emphasizes gratitude and focus on learning.
Invocation for the Holy Spirit to guide understanding and practical application of lessons.

Geometric Shapes

Geometry topics include rectangle, parallelogram, square, kite, trapezoid, and rhombus.

Number Classifications

Identified classifications:
- Composite number (e.g., 2, 4, 15, 21)
- Even number (4, 2)
- Odd number (11, 15, 21)
- Prime number (11, 15)

Functions and Relations

A relation consists of ordered pairs; domain is the first coordinate set, range is the second coordinate set.
A function relates each element of the domain to exactly one element in the range.

Characteristics of Functions

Each element in the domain (X) maps to only one element in the range (Y).
Some elements in the range may not correspond to any element in the domain.
Multiple elements in the domain can map to the same element in the range.
No element in the domain can map to more than one different element in the range.

Representations of Functions

Functions can be represented through:
- Mapping diagrams
- Set of ordered pairs
- Tables
- Graphs

Vertical Line Test

A graph represents y as a function of x if no vertical line crosses the graph in more than one location.

Evaluating Functions

Example evaluations for functions:
- For (f(x) = 3x):
  - (f(4) = 12)
  - (f(-6) = -18)
- Additional examples listed for different values of x.

Real-Life Applications of Functions

Mikha’s salary calculation based on daily earnings.
- (f(x) = 585x) for 22 days results in a monthly salary of 12,870.
Aiah’s walking speed calculation.
- (f(x) = 7x) calculating distance traveled over 3 hours gives 21 km.
Height measurement after dropping a ball.
- Function (h(t) = 5.8t + 72) calculates height after 5 seconds as 217 m.

Operations on Functions

Sum of Functions:
- Defined for overlapping domains; algebraic expression for addition.
Difference of Functions:
- Similar definition focusing on subtraction.
Product of Functions:
- Multiplication of function values; example evaluations provided.
Quotient of Functions:
- Division of function values, with examples and evaluations included.

Activity Task

Students are tasked with creating examples for each operation on functions and solving them, demonstrating understanding of the material.

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Description

Test your understanding of general mathematics concepts with this quiz led by Ms. Rose Ann P. Ramos. Gain insights and discover practical applications of mathematics in everyday activities as you enhance your learning experience.