# What is the domain and range of #f(x) =(x-3)/(7x+4)#?

##### 2 Answers

#### Explanation:

So this is a rational function, so to get

So your quotient,

Therefore,

Rearrange this to make your solution of the form

Therefore,

This means that you have asymptotes at

#### Explanation:

#"f(x) is defined for all real values of x apart from values that"#

#"make the denominator equal to zero"#

#"equating the denominator to zero and solving gives the"#

#"value that x cannot be"#

#"solve " 7x+4=0rArrx=-4/7larrcolor(red)" excluded value"#

#rArr"domain is " x inRR,x!=-4/7#

#"to find any excluded value in the range, rearrange "#

#y=f(x)" making x the subject"#

#rArry(7x+4)=x-3larrcolor(blue)" cross-multiplying"#

#rArr7xy+4y=x-3#

#rArr7xy-x=-3-4y#

#rArrx(7y-1)=-(3+4y)#

#rArrx=-(3+4y)/(7y-1)#

#"the denominator cannot equal zero"#

#"solve " 7y-1=0rArry=1/7larrcolor(red)" excluded value"#

#rArr"range is " y inRR,y!=1/7#