Questions and Answers
What is the formula to compute the average speed of a runner?
s = d/t
What function represents the speed of a runner as a function of time for a 100-meter track?
s(x) = 100/x
What are the run times used to create the table of values for the runner's speed?
10, 12, 14, 16, 18, 20 seconds
The speed decreases with ______.
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Which of the following values corresponds to a run time of 14 seconds based on the table?
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The points from the table of values connect to form a straight line.
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What is the function represented by f(x) = (x - 1)?
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What happens to the speed of a runner as the time taken to complete the 100 meters increases?
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What is the speed of a runner who takes 12 seconds to complete the 100-meter track?
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At what time does the speed of a runner reach 5 m/s based on the provided table?
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Which of the following points indicates the speed of the runner at 16 seconds?
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What is the behavior of the function f(x) = (x - 1)/(x + 1) at x = -1?
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Which characteristic describes the graph formed by connecting the points for the runner's speed over time?
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What x-value leads to a speed of 7.14 m/s according to the table?
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When graphing the function f(x) = (x - 1)/(x + 1), which x-value should not be included in the graph?
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Study Notes
Overview of Self-Learning Kit
- Designed for Grade 11 Senior High School students to enhance understanding of General Mathematics.
- Aligns with the BEC of the Department of Education and adheres to MELCs (Most Essential Learning Competencies).
- Features pre-activities for reviewing prior knowledge and measuring learning through pretests.
Learning Objectives
- Represent rational functions while determining domain, range, intercepts, zeroes, and asymptotes.
- Solve equations and inequalities involving rational functions.
- Develop problem-solving perseverance related to rational functions.
Representing Real-Life Situations with Rational Functions
- Average speed formula: ( s = \frac{d}{t} ). In a 100-meter scenario, this can be represented by ( s(x) = \frac{100}{x} ), where ( x ) is time.
- A table of values for runner's speed from 10 to 20 seconds shows speed decreases as time increases:
- Values: ( x ): 10, 12, 14, 16, 18, 20
- Corresponding ( s(x) ): 10, 8.33, 7.14, 6.25, 5.56, 5
Graphing Functions
- Graphing the function involves plotting points from the table created from the runner's speed.
- Points plotted on Cartesian plane:
- ( A(10, 10) )
- ( B(12, 8.33) )
- ( C(14, 7.14) )
- ( D(16, 6.25) )
- ( E(18, 5.56) )
- ( F(20, 5)
- Connecting the points reveals a smooth curve, indicating a nonlinear relationship between speed and time despite appearing collinear at first glance.
Example of a Rational Function
- Given rational function ( f(x) = \frac{x-1}{x+1} ) should also be represented using a table of values and graphical representation, similar to the speed example provided.
Average Speed and Rational Functions
- Average speed is calculated using the formula ( s = \frac{d}{t} ).
- For a 100-meter track, speed can be expressed as ( s(x) = \frac{100}{x} ), where ( x ) is the time taken to complete the distance.
Speed Table and Observations
- A table of values for times from 10 to 20 seconds shows corresponding speeds:
- ( x = 10 ) seconds, ( s(x) = 10 ) m/s
- ( x = 12 ) seconds, ( s(x) = 8.33 ) m/s
- ( x = 14 ) seconds, ( s(x) = 7.14 ) m/s
- ( x = 16 ) seconds, ( s(x) = 6.25 ) m/s
- ( x = 18 ) seconds, ( s(x) = 5.56 ) m/s
- ( x = 20 ) seconds, ( s(x) = 5 ) m/s
- Speed decreases as time increases, indicating an inverse relationship.
Graphing the Speed Function
- Points plotted on a Cartesian plane include:
- ( A(10, 10) )
- ( B(12, 8.33) )
- ( C(14, 7.14) )
- ( D(16, 6.25) )
- ( E(18, 5.56) )
- ( F(20, 5) )
- Points connect to form a smooth curve, demonstrating a decrease in speed with increased time.
Rational Functions Example
- The function ( f(x) = \frac{x-1}{x+1} ) is considered for further exploration.
- A table of values is constructed for ( x ) ranging from -10 to 10.
- The function is undefined at ( x = -1 ), causing a discontinuity in the graph.
- It is essential to represent the graph accurately by omitting the segment between points corresponding to ( x = -1 ).
Summary of Concepts
- The relationship between speed and time illustrates the nature of rational functions.
- Graphing helps visualize the behavior of functions, including discontinuities.
- Understanding how to represent functions through tables and graphs is essential in analyzing rational functions.
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Description
This quiz focuses on functions as part of the General Mathematics curriculum for Senior High School, specifically for Grade 11 students. It aims to enhance understanding and application of mathematical concepts in functions, which is essential for further learning in mathematics.
