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Precalculus 1.1 Functions And Function Notation Questions And Answers Latest Update
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Precalculus 1.1 Functions And Function Notation Questions And Answers Latest Update

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  • November 4, 2024
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  • 2024/2025
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Precalculus 1.1 Functions And
Function Notation Questions And
Answers Latest Update

relation ANS✔✔ a set of ordered pairs


domain ANS✔✔ The set of the first numbers of the ordered pairs in a
relation or the input value


range ANS✔✔ the set of second numbers of the ordered pairs in a relation or
the output value


Look at a set of ordered pairs. {(1,2),(2,4),(3,6),(4,8),(5,10)} The first numbers
in each pair are the first five natural numbers. The second number in each pair
is twice that of the first. What is the domain and range? ANS✔✔ The domain
is {1, 2, 3, 4, 5}. The range is {2,4,6,8,10}.


input value, or independent variable ANS✔✔ Each value in the domain,
which is often labeled with the lowercase letter 𝑥.


output value, or dependent variable ANS✔✔ Each value in the range, which
is often labeled lowercase letter 𝑦.

, A function𝑓 ANS✔✔ A function is a relation in which each possible input
value leads to exactly one output value. It assigns a single value in the range to
each value in the domain. We say "the output is a function of the input." In
other words, no x-values are repeated.


Is {(1,2),(2,4),(3,6),(4,8),(5,10)} a function? ANS✔✔ For our example that
relates the first five natural numbers to numbers double their values, this
relation is a function because each element in the domain, {1, 2, 3, 4, 5}, is
paired with exactly one element in the range, {2, 4, 6, 8, 10}.


Is {(odd,1),(even,2),(odd,3),(even,4),(odd,5)} a function? ANS✔✔ each
element in the domain, {even, odd} is not paired with exactly one element in
the range, {1, 2, 3, 4, 5}. For example, the term "odd" corresponds to three
values from the range, {1, 3, 5} and the term "even" corresponds to two values
from the range, {2, 4}. This violates the definition of a function, so this relation
is not a function.


HOW TO
Given a relationship between two quantities, determine whether the
relationship is a function. ANS✔✔ 1) Identify the input values and the
output values.
2) If each input value leads to only one output value, classify the relationship
as a function.
3) If any input value leads to two or more outputs, do not classify the
relationship as a function.


The coffee shop menu consists of items and their prices. Is price a function of
the item? Is the item a function of the price?
item. price

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