Home > Algebra > Domain and Range of a Function

What is the range of the function #y=-3/(4x+4)#?

Answer 1

Savannah Anderson

#y inRR,y!=0#

#"rearrange making x the subject"#

#y=-3/(4x+4)#

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

#rArr4xy+4y=-3larr" distributing"#

#rArr4xy=-3-4y#

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

#"the denominator cannot equal zero as this would make"# #"the function undefined"# #"equating the denominator to zero and solving gives the"# #"value that y cannot be"#

#"solve "4y=0rArry=0larrcolor(red)" excluded value"#

#rArr"range is " y inRR,y!=0#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Julia Adams

To find the range of the function ( y = -\frac{3}{4x + 4} ), first, we need to consider the domain of the function. Since the denominator ( 4x + 4 ) cannot be zero, we have ( x \neq -1 ) as the domain.

Now, as ( x ) approaches infinity, ( y ) approaches zero. As ( x ) approaches negative infinity, ( y ) also approaches zero. Thus, the range of the function is all real numbers except zero.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.