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Determine if the following is a function, and if it is a one-to-one function.

{(9,0),(7,7),(7,5),(5,9),(8,8)}
Not a function
A function, not one-to-one
A one-to-one function

Determine if the following is a function, and if it is a one-to-one function. $\newline$ $\{(9,0),(7,7),(7,5),(5,9),(8,8)\}$ $\newline$ Not a function $\newline$ A function, not one-to-one $\newline$ A one-to-one function

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Intermediate Value Theorem

Full solution

Q. Determine if the following is a function, and if it is a one-to-one function.

\newline

\{(9,0),(7,7),(7,5),(5,9),(8,8)\}

\newline

Not a function

\newline

A function, not one-to-one

\newline

A one-to-one function

Check Input-Output Mapping: To determine if the given set of ordered pairs represents a function, we need to check if each input (first component of each ordered pair) maps to exactly one output (second component of each ordered pair).
Examine Ordered Pairs: Examine the set of ordered pairs: ${(9,0),(7,7),(7,5),(5,9),(8,8)}$ . We notice that the input $'7'$ is associated with two different outputs: $'7'$ and $'5'$ .
Identify Multiple Outputs: Since the input $7$ maps to more than one output, the set of ordered pairs does not represent a function. $\newline$ We can stop here as the definition of a function is not satisfied.

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