A. Read and analyze the following statements. If you think the statement suggests an incorrect idea, rewrite it on the given space, otherwise leave it blank.
1. A relation is a set of ordered pairs where the first element is called the range while the second element is the domain.
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2. A function can be classified as one-to-one correspondence, one-to-many correspondence and many-to-one correspondence.
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3. In a function machine, the input represents the independent variable while the output is the dependent variable.
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B. In three to five sentences, write the significance of function in showing real-life situations.
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C. In your own words, discuss when a piecewise function is being used.
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Answers
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1. False.
A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range.
2. True.
A function can be classified as one-to-one correspondence and many to one correspondence, it couldn't be one too many because a relation to be considered as a function shouldn't have the same domain.
3. True.
The function is the “machine” or the rule that tells us how to use the input to make an output. Variables are used to represent values we don't know or that may change. For a function, the input is called the independent variable, and the output is called the dependent variable.
B. Ans: Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies, and for keeping airplanes in the air. Functions can take input from many variables, but always give the same output, unique to that function.
C. Ans: We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value.