Domain of a rational equation

Question

anonymous · Answer

$$\frac{ (x+2)(x-1) }{ (x-4)(x+1) }$$

anonymous · Answer

Is it -2 and 1?

freckles · Answer

domain of the rational expression is all real numbers except for the numbers that make the bottom zero

anonymous · Answer

I mean range oops

anonymous · Answer

The domain is 4, -1

freckles · Answer

well the domain would be all real numbers except x=4 or x=-1

anonymous · Answer

How do I get the domain?

freckles · Answer

the domain is all the x values for which the function exists

freckles · Answer

the fraction doesn't exist when the bottom is zero

anonymous · Answer

Range I mean

freckles · Answer

the range is the y values of the function where the function exists

anonymous · Answer

So is it usually the same answer as the domain?

freckles · Answer

well the domain is the set of x values where the function exists
the range is the set of y values where the function exists
the range will not always equal the domain
since they represent different sets

anonymous · Answer

If there is no x values in the top is the range all real numbers?

anonymous · Answer

Compared to the question I was given
$$\frac{ (x+2)(x-1) }{ (x-4)(x+1) }$$
The domain is all real numbers except for 4 and -1
Is the range all real numbers except for 4 and -1 as well?

anonymous · Answer

@Nnesha @geerky42

freckles · Answer

no

freckles · Answer

Hint: Look at your graph if you can. If you can't consider what happens at your vertical asymptotes and consider your horizontal asymptotes...And ask yourself can the number that is the horizontal asymptote also be hit for the graph given.