Math Grade 8: Variables and Functions
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Questions and Answers

Which of the following refers to the value of output in a function?

  • Abscissa
  • Constant
  • Dependent variable (correct)
  • Independent variable

    • Marites wants to know the effect of the new fertilizer on the growth of her plants. In the situation, what is the independent variable?

  • The new fertilizer and plant growth
  • Marites' Experiment
  • The growth of plants
  • The new fertilizer (correct)

    • In a set of ordered pairs (xi, yi), what do you call the set of the first coordinates?

  • x-axis
  • Range
  • y-axis
  • Domain (correct)

    • In a set of ordered pairs (xi, yi), what do you call the set of the second coordinates?

    <p>Range</p> Signup and view all the answers

    What is the domain of the set of ordered pairs {(1, 2), (2, 4), (3, 6), (4, 8)}?

    <p>{1, 2, 3, 4}</p> Signup and view all the answers

    What is the range of the set of ordered pairs {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}?

    <p>{0, 1, 2, 4}</p> Signup and view all the answers

    What is the domain of the diagram shown at the right?

    <p>{-3, 0, 3, 5}</p> Signup and view all the answers

    Using the diagram in #7, what is the range?

    <p>{-3, 0, 2, 5}</p> Signup and view all the answers

    Mary Ann helped her mother in selling banana cue. Each banana cue costs Php5. The amount of money she makes is a function of the number of banana cue. What is the domain of the function if she has 10 banana cues to sell?

    <p>Domain: {0, 1, 2, ..., 9, 10}</p> Signup and view all the answers

    Consider the situation in # 9, what is the range of the function?

    <p>Range: {1, 2, 3, ..., 9, 10}</p> Signup and view all the answers

    The table at the right describes y as a function of x. Which of the following correctly describes the value of -3?

    <p>It is part of the range</p> Signup and view all the answers

    Observe the figure at the right. The number of squares that make up the figures is a function of the indicated figure number. Which of the following statements is true?

    <p>The domain is the set {1, 2, 3} while range is the set {1, 4, 9}</p> Signup and view all the answers

    In figure 1 at the right, the domain is {x ∈ R | x ≥ -3} because the graph extends horizontally to

    <p>The right</p> Signup and view all the answers

    Using figure 1 in item 13, the range of the function is {y ∈ R | y ≤ 2} because the graph discontinued at 2 and extends vertically

    <p>Downward</p> Signup and view all the answers

    Which graph below describes the domain D = {x ∈ R | x ≥ -4}?

    Signup and view all the answers

    Determine the two variables in the scenario: In order to earn some money, Robert cleans his neighbor's backyard for several hours during weekends. How much money did he earn?

    <p>Number of hours Robert works and amount of money Robert earns.</p> Signup and view all the answers

    Which of the variables could be changed independently?

    <p>Number of hours cleaning</p> Signup and view all the answers

    Which of the variables could be affected by the change of the other?

    <p>Amount of money earned</p> Signup and view all the answers

    The ______ (number of hours cleaning/amount of money earned) is the independent variable because it ______ (controls/depends on) the ______ (number of hours cleaning/amount of money earned).

    <p>number of hours cleaning, controls, amount of money earned</p> Signup and view all the answers

    If for every hour he gets paid Php40, how much will he earn after working 5 hours?

    <p>Php200</p> Signup and view all the answers

    Would it be possible for Robert to earn Php800.00 in one day? Why or why not?

    <p>False</p> Signup and view all the answers

    Which of the following statements is TRUE about the diagram shown in #5?

    <p>-1 is part of the domain</p> Signup and view all the answers

    In a park, Donny wants to rent a bicycle for his son. The rental of bicycle is P20/hour. The amount of rental is a function of the number of hours his son will use the bicycle. What is the domain of the function if they are to stay in the park for 4 hours?

    <p>Domain: {0, 1, 2, 3, 4}</p> Signup and view all the answers

    Given a folded piece of paper, the number of rectangles formed depends on the number of folds it has (as shown in the table below). Which of the following statements is true?

    <p>The domain is the set {1, 2, 3, 4, ...}</p> Signup and view all the answers

    What is the domain of the graph shown in figure 2?

    <p>{-4, -2, 0, 3, 4}</p> Signup and view all the answers

    In figure 3 at the right, the domain is {x ∈ R} because the graph extends horizontally to

    <p>The right</p> Signup and view all the answers

    What is the range of the graph shown in figure 3?

    <p>R = {y ∈ R | y ≥ -3}</p> Signup and view all the answers

    Which graph below describes the range R = {y ∈ R| y ≤ 4}?

    Signup and view all the answers

    What is the domain of the function f(x) = √2x - 2?

    <p>Domain = {x ∈ R | x ≥ 1}</p> Signup and view all the answers

    What is the range of the function f(x) = (x + 1)/2x?

    <p>Range = {y ∈ R | y ≠ 1/2}</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). In the given situation, the number of liters of gasoline is what type of variable? Why?

    <p>Independent Variable</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). In the given situation, the amount paid is what type of variable? Why?

    <p>Dependent Variable</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). What is the domain of the function?

    <p>The domain of the function is {x ∈ R| 0 ≤ x ≤ 7}.</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). Can 5.5 liters of gasoline be the domain in the situation? Explain.

    <p>True</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). Can Php350 an acceptable value of range in the situation? Explain.

    <p>False</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). What could be the domain and range if the tank is quarter full before he had to fill it with gasoline?

    <p>The domain could be {x ∈ R| 1.75 &lt; x ≤ 7} and the range could be {y ∈ R| 80.50 ≤ y ≤ 322}.</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). Is it possible to fill the tank with 7.2 liters of gasoline? Why? Why not?

    <p>False</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). Noli is sitting on his motorcycle while allowing the gasoline station attendant to fill the tank. Is it correct? Why? Why not?

    <p>False</p> Signup and view all the answers

    Noli has to fill up his motorcycle with gasoline to travel from Barobo to Tandag City. The maximum capacity of the fuel tank of his motorcycle is 7 liters and the gasoline price is Php46 per liter. The amount paid (y) is a function of the number of liters of gasoline (x). If you are in the situation of Noli, what safety precautions would you observe while refuelling your motorcycle?

    <p>Turn off the engine, dismount the motorcycle, move a safe distance away from the area, and avoid smoking or using a mobile phone while refuelling. Once done, check for leaks and ensure the fuel cap is securely closed.</p> Signup and view all the answers

    Given the variables: the cost to rent an apartment and the length of time it is rented, which is the independent variable?

    <p>The length of time it is rented</p> Signup and view all the answers

    The price of powdered milk is a function of its net weight. In the function, the price of powdered milk is called

    <p>Outputs</p> Signup and view all the answers

    What is the domain of the given set of ordered pairs {(3, 1),(2, 5), (0, 5), (-2, 6), (-4, 7)}?

    <p>{3, 2, 0, -2, -4}</p> Signup and view all the answers

    The teacher asked John to determine the range of the given set of ordered pairs {(1, 1), (2, 4), (3, 4), (-2, 1), (-4, 5)}. His answer is {1, 1, 4, 4, 5}. Is he correct?

    <p>No, because the elements should be written once and the answer is {1, 4, 5}</p> Signup and view all the answers

    The dependent variable changes only in response to the independent variable.

    <p>True</p> Signup and view all the answers

    Salary is an independent variable because it controls the number of hours that one works.

    <p>False</p> Signup and view all the answers

    The height of a plant is dependent on the number of years it grown.

    <p>True</p> Signup and view all the answers

    In a given function, the domain is the set of acceptable inputs while the range is the set of acceptable outputs.

    <p>True</p> Signup and view all the answers

    In a set of ordered pairs, the abscissas are the range and the ordinates are the domain.

    <p>False</p> Signup and view all the answers

    In a rational function, f(x) = 1/2x, the domain is the set of real numbers not equal to the number that would make the denominator zero.

    <p>True</p> Signup and view all the answers

    In a rational function, f(x) = 1/2x, the range is the set of real numbers except zero.

    <p>True</p> Signup and view all the answers

    In a radical function, f(x) = 2√x + 1, the domain is the set of real numbers greater than or equal to 0.

    <p>True</p> Signup and view all the answers

    Study Notes

    Module Information

    • Module Title: Determining the Dependent and Independent Variables and Finding the Domain and Range of a Function
    • Grade Level: 8
    • Subject: Mathematics
    • Quarter: 2
    • Module Number: 6

    Key Concepts

    • Independent Variable: A variable that can change independently of other variables. It's the variable that is manipulated or controlled.
    • Dependent Variable: A variable that depends on the independent variable. Its value changes as the independent variable changes.
    • Domain: The set of all possible input values (x-values) for a function.
    • Range: The set of all possible output values (y-values) for a function.

    Finding Variables

    • Identify the quantities that change in a given situation.
    • One variable can be affected by the other.

    Finding Domain and Range

    • From Ordered Pairs: The domain is the set of x-values, and the range is the set of y-values. List each in ascending order, but only repeat a value once.
    • From Mappings/Graphs:
    • Domain: Identify the individual x-values shown in the mapping/graph.
    • Range: Identify the individual y-values shown.
    • From Function Rules: Identify acceptable input values (x-values) that do not result in undefined operations in the function. Identify the resulting output (y-values)
    • Real-Life Situations: Determine the reasonable values for the independent and dependent variables for a given situation, avoiding impossible/irrational values

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    Mathematics 8 Quarter 2 Module 6 PDF

    Description

    This quiz focuses on determining independent and dependent variables, as well as finding the domain and range of functions. Students will practice identifying these concepts through various mathematical scenarios. Enhance your understanding of these foundational concepts essential for mastering functions.

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