Q57. - Algebra 1

Question

Determine which of the following relations is a function.

F $\left\{(-3,2),(4,1),(-3,5)\right\}$

G $\left\{(2,-1),(4,-1),(2,6)\right\}$

H $\left\{(-3,-4),(-3,6),(8,-2)\right\}$

J $\left\{(5,-1),(3,-2),(-2,-2)\right\}$

Step-by-Step Solution

Answer

J is a function.

Step 1. Given.

The given functions are,

F $\left\{(-3,2),(4,1),(-3,5)\right\}$ 

G $\left\{(2,-1),(4,-1),(2,6)\right\}$

H $\left\{(-3,-4),(-3,6),(8,-2)\right\}$ 

J $\left\{(5,-1),(3,-2),(-2,-2)\right\}$

Step 2. To determine.

Which of the given relation is a function.

Step 3. Calculation.

A relation is called a function if the following conditions are satisfied:

 

1) Every value in its domain has a unique value in its codomain.

2) For every value of $x$, there is a unique value of $y$.

3) For every value of $x$, there must be only one value of $y$.

 

Considering the relation F. F is $\left\{\left(-3,2\right)\left(4,1\right)\left(-3,5\right)\right\}$.

The element $-3$ of domain is paired with 2 and 5 of range. So, F is not a function.

 

Considering the relation  G. G is $\left\{\left(2,-1\right)\left(4,-1\right)\left(2,6\right)\right\}$.

The element 2 of domain is paired with $-1$ and 6 of range. So, G is not a function

 

Considering the relation  H. H is $\left\{\left(-3,-4\right)\left(-3,6\right)\left(8,-2\right)\right\}$.

The element $-3$ of domain is paired with $-4$ and 6 of range. So, H is not a function.

 

Considering the relation  J. J is $\left\{\left(5,-1\right)\left(3,-2\right)\left(-2,-2\right)\right\}$.

One element of the domain is paired with only one element of the range. So, J is a function.

 

Hence, the correct option is (J).