Questions and Answers
What is the result of expanding the binomial $4x^2 + 2x + 1 - 5(x + 1)$?
The expression $(f - g)(x)$ results in a polynomial of degree 2.
True
What is the simplified form of $(g ullet f)(x)$?
It cannot be determined from the provided information.
When combining like terms in the expression $(f - g)(x)$, the result is _____.
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Match the expressions with their correct operations or definitions:
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What is the value of f(0) when the function is defined as f(x) = 2x - 3?
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The velocity of the ball is increasing over time.
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What is the expression for f(m)?
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The velocity of the ball after 1 second is _____ m/s.
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What is the value of f(5)?
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F(x - 1) simplifies to _____ after simplification.
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Match the following values with their corresponding f(x) results:
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How much profit does the company make if they sold 300 bags?
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What is the value of $f(3)$ for the function $f(x) = x^3 + x^2 + 3x - 12$?
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What is the price of a single Cadbury chocolate bar if you buy 20 or fewer?
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The function $f(x + 1)$ is equal to $f(x - 2)$ for the given function.
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What is the product of the functions $f(x) = 2x^2 + 3$ and $g(x) = x^2 - 2x$?
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If you buy more than 20 chocolate bars, each bar costs Php10.00.
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What is the cost for using a computer for 4 hours at the ML computer shop?
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The difference of the functions $f(x)$ and $g(x)$ is defined as $(f - g)(x) = f(x) + g(x)$.
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If a customer uses the computer for 45 minutes, they pay __________.
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Express the total salary (S) as a function of the number of days (n) for a person earning Php390.00 per day.
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What operation is defined for the sum of two functions?
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If $f(x) = 4x^2 - 1$ and $g(x) = 2x^2 + 3x + 1$, then the quotient of the functions is given by (f / g)(x) = ____.
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A taxi ride costs Php ______ as the flag-down rate.
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What is $f(7)$ for the function $f(x) = x^3 + x^2 + 3x - 12$?
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What is the additional cost for each meter after the flag-down rate in a taxi ride?
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Match the following operations with their definitions:
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Match the computation with the computer shop charges:
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What is the value of $f(x + 1)$ for $f(x) = x^3 + x^2 + 3x - 12$?
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The cost of a taxi ride does not increase with the distance traveled.
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For usage beyond two hours, ML computer shop charges Php __________ for each additional hour.
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Match the following items with their respective costs:
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What kind of function can be used to represent the cost of chocolate bars when buying 20 or fewer versus more than 20?
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Study Notes
Piecewise Functions
- A Cadbury chocolate bar costs Php12.00 each but drops to Php10.00 if over 20 pieces are purchased.
- The cost as a function:
- If n ≤ 20, Cost = 12n
- If n > 20, Cost = 10n
Salary as a Function
- Daily earnings of Php390.00 can be expressed as a total salary function S(n):
- S(n) = 390n, where n is the number of days worked.
Taxi Fare Calculation
- Initial flag-down rate for a taxi is Php40.00, with an additional Php4.00 for each meter.
- The fare function based on distance d:
- Fare(d) = 40 + 4(d - 1) for d meters.
Function Evaluation
- For f(x) = x³ + x² + 3x - 12, evaluate:
- f(3) = 3³ + 3² + 3(3) - 12 = 36
- f(7) = 7³ + 7² + 3(7) - 12 = 336
- f(x + 1) = (x + 1)³ + (x + 1)² + 3(x + 1) - 12
- f(x² - 1) = (x² - 1)³ + (x² - 1)² + 3(x² - 1) - 12
- Check if f(x + 1) equals f(x - 2).
Computer Shop Charges
- Charges are Php30.00 for the first two hours and Php15.00 for each additional hour.
- For services:
- 45 minutes = Php30.00
- 4 hours = Php75.00 (Php30 for 2 hours + Php15 for each of the next 2 hours)
- 155 minutes = Php45.00 (Php30 for 2 hours + Php15 for extra 55 minutes).
Profit Calculation for Manufacturing
- Profit function is given as f(x) = 3x + 250, where x is the number of bags sold.
- Calculate profit for 300 bags:
- Profit = 3(300) + 250 = Php1,150.
Operations on Functions
- For functions f(x) = 2x² + 3 and g(x) = x² - 2x:
- Sum: (f + g)(x) = f(x) + g(x) = 3x² + 3.
- Difference: (f - g)(x) = f(x) - g(x) = x² + 5x + 3.
Quotient of Functions
- If f(x) = 4x² - 1 and g(x) = 2x² + 3x + 1:
- (f / g)(x) = (4x² - 1) / (2x² + 3x + 1).
Composition of Functions
- For f(x) = 6x² - 14x + 3 and g(x) = 2x² + 6x - 2:
- Find (f - g)(x) = 4x² - 20x + 5.
- Composition g(f(x)): Replace x in g(x) with f(x).
General Notes
- A relation is defined as a set of ordered pairs.
- Piecewise functions are used to define scenarios with different conditions.
- Understanding function evaluation, composition, and operations is crucial for problem-solving in mathematics.
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Description
This quiz focuses on applying piecewise functions to solve real-world problems, specifically in calculating the cost of chocolate bars. You will analyze the pricing structure based on quantity purchased, honing your numeracy skills in the process. Prepare to showcase your understanding of mathematical concepts through practical application.
