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Look at this set of ordered pairs: $\newline$ $(10, 9)$ $\newline$ $(3, 17)$ $\newline$ $(3, 8)$ $\newline$ Is this relation a function? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Identify functions

Full solution

Q. Look at this set of ordered pairs:

\newline

(10, 9)

\newline

(3, 17)

\newline

(3, 8)

\newline

Is this relation a function?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand Function Definition: Step $1$ : Understand the definition of a function. $\newline$ A relation is a function if each input ( $x$ -value) has exactly one output ( $y$ -value). Let's check if each $x$ -value in the set of ordered pairs has only one corresponding $y$ -value.
List $X$ and $Y$ Values: Step $2$ : List all $x$ -values and their corresponding $y$ -values. $\newline$ From the ordered pairs: $\newline$ - $(10, 9)$ $\newline$ - $(3, 17)$ $\newline$ - $(3, 8)$ $\newline$ We see that the $x$ -value $3$ corresponds to two different $y$ -values ( $Y$ $0$ and $Y$ $1$ ).
Determine Function Status: Step $3$ : Determine if the relation is a function. $\newline$ Since the $x$ -value $3$ maps to more than one $y$ -value, this violates the definition of a function. Therefore, the relation is not a function.

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\newline

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