Domain and range...help?!

Question

Help please!!

Identify domain and range for the graph of:

y= 5/x-3 +2

Answer 1

y = 5 / ( x - 3 ) + 2

Domain :

x can take all real values except 3 because if x=3 the denominator x-3 will be equal zero, and that is lead that the value of y =∞ , so the domain is:

( - ∞ , 3 ) U ( 3 , ∞ ) , we have vertical asymptote at x=3.

Range:

For the range we can take the limit and find the value of y when x→ ∞ , and when x→- ∞

y = 5 / ( x - 3 ) + 2

= [ 5 + 2 (x -3) ] / ( x -3 ) = 5 +2x -6 / ( x-3) = 2x - 1 / ( x - 3 )

lim _{x → ∞} y = lim _{x → ∞} 2x -1 / x -3 = 2x/x = 2

lim _{x → - ∞} y = 2x / x = 2

That is mean y can take all real values except 2.

Range ( - ∞ , 2 ) U ( 2 , ∞ ) and that is mean we have a horizontal asymptote at y = 2

Answer 2

In this equation: y= 5/(x-3) +2, y cannot = 3 because you cannot divide by zero. x can be any other real number.

Domain: (−∞,3)∪(3,∞),{x|x≠3}

Range: (−∞,2)∪(2,∞),{y|y≠2}