Given the equation of xy - 5y = 2x + 3

Question

show that y is a function of x and determine the domain in interval notation 

Answer 1

The equation

To determine the above rational expression is function.

Substitute x = 0, 1 , 2, -1, -2 respectively then find the set of coordinate pair.

For x  = 0

For x  = 1

For x  = 2

For x  = - 1

For x  = - 2

We know that x  values are domain and y values is range of a function.

The coordinates pairs are

 

We can able to write, domain set is

Range set is

A  function  is a special type of relation in which each element of the domain is paired with exactly one element of the range.

The relation is  a function because the each element of the domain is paired with exactly one element of the range.

Therefore, is a function .

Answer 2

Contd....

The rational function

We know that all possible values of x  is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find, which number make the fraction undefined create an equation where the denominator is not equal to zero.

So, the domain of the function is all real numbers except 5.

Domain set is

Domain in interval notation .