# How do you find the domain and range and determine whether the relation is a function given {(-2,5), (3,7), (-2,8)}?

Feb 9, 2018

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{D o m a \in\right\} = \setminus \left\{- 2 , - 3 , - 2 \setminus\right\} .$

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{R a n \ge\right\} \setminus \quad = \setminus \left\{5 , 7 , 8 \setminus\right\} .$

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{R e l a t i o n i s a F u n c t i o n .\right\}$

#### Explanation:

$\setminus m b \otimes \left\{G i v e n S e t o f O r \mathrm{de} red P a i r s =\right\} \setminus \quad \setminus \left\{\begin{matrix}- 2 & 5 \\ - 3 & 7 \\ - 2 & 8 \setminus\end{matrix}\right\}$

$\setminus m b \otimes \left\{D o m a \in = S e t o f F i r s t C \infty r \mathrm{di} n a t e s\right\} \setminus \quad = \setminus q \quad \setminus \quad \setminus \setminus \left\{- 2 , - 3 , - 2 \setminus\right\}$

$\setminus \quad \setminus m b \otimes \left\{\left(r e m o v \in g \mathrm{du} p l i c a t e e n t r i e s w i t h \in a s e t\right)\right\} \setminus q \quad = \setminus \quad \setminus \left\{- 2 , - 3 \setminus\right\} .$

$\setminus m b \otimes \left\{R a n \ge = S e t o f S e c o n d C \infty r \mathrm{di} n a t e s\right\} \setminus \quad = \setminus q \quad \setminus \quad \setminus \setminus \left\{5 , 7 , 8 \setminus\right\} .$

 \mbox{A Relation is a Function precisely when there are no repeated} \ \ \mbox{first coordinates. Scanning the first coordinates of the Relation,} \ \mbox{we see that the first coordinate -2 is repeated !!} \ \mbox{So the Relation is not a Function.}

$\setminus$

$\setminus m b \otimes \left\{S u m m a r y\right.$

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{D o m a \in\right\} = \setminus \left\{- 2 , - 3 , - 2 \setminus\right\} .$

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{R a n \ge\right\} \setminus \quad = \setminus \left\{5 , 7 , 8 \setminus\right\} .$

$\setminus q \quad \setminus q \quad \setminus m b \otimes \left\{R e l a t i o n i s a F u n c t i o n .\right\}$