Whats the domain and range for
f(x)= x^2+x-2/x^2-3x-4

Question

Whats the domain and range for
f(x)= x^2+x-2/x^2-3x-4

arindameducationusc · Answer

Well for domain, the roots of the denominator should not be zero.

anonymous · Answer

Is the domain all real numbers except for -1, and 4?

anonymous · Answer

and is the range 1?

anonymous · Answer

so the numerator and denominator are 2 different domains?

usukidoll · Answer

the domain is in the x-axis and the range is in the y-axis. Since we are given a fraction as a function there is going to be restrictions in the domain.

usukidoll · Answer

$$(x^2-3x-4) \rightarrow (x+1)(x-4)$$
so the domain should be all real numbers except when x = -1 and x = 4. which is what I saw earlier. so yes you're correct on that one @Abbs__

usukidoll · Answer

that doesn't sound right at all ^

usukidoll · Answer

@Michele_Laino

anonymous · Answer

Thanks!

arindameducationusc · Answer

Yes Yes, I did a calculation mistake, @Abbs_ is right

anonymous · Answer

It's okay. :)

usukidoll · Answer

range is going to be a little bit harder though...

anonymous · Answer

Is it all real numbers except y=1?

usukidoll · Answer

I gotta be honest. I have to graph that function first.. and desmos hates me and my fractions

michele_laino · Answer

I agree with the answer of @UsukiDoll

usukidoll · Answer

thanks, HEY YOUR QH symbol is back @Michele_Laino !

michele_laino · Answer

yes! I see nevertheless not in mathematics subsections, thanks! @UsukiDoll

usukidoll · Answer

attachment

usukidoll · Answer

the line has to cover the y-values ... if the line doesn't cover the y-values then we have a restriction. This is where I fumble a lot. It could be all reals except y = 1... not sure. What do you think @Michele_Laino

michele_laino · Answer

at points where the function is undefined, generally that function behaves as an infinity, and that is what is happening into your graph

usukidoll · Answer

so it's all reals for the range?

usukidoll · Answer

it's like every time I do these problems, I understand the domain no problem. I see the gaps. It's the range that's frustrating.

michele_laino · Answer

the range, as in this case, is always a real set, nevertheless is not a limited set

usukidoll · Answer

because it goes on forever?

michele_laino · Answer

yes!

usukidoll · Answer

|dw:1437990839458:dw| ok.. so consider this drawing of a circle .. would the domain be from -1 to 1 and then range be -1 to 1 as well.

michele_laino · Answer

towards down or towards up

arindameducationusc · Answer

yes, range should be -1 to 1

arindameducationusc · Answer

y-axis represents Range

michele_laino · Answer

your function is a circular function, so its domain is the subsequent set:
$$\Large [0,2\pi )$$

usukidoll · Answer

*I'm not going for trig... just regular domain and range*

michele_laino · Answer

in order to establish the range, we need to know the exact algebraic shape of your function

arindameducationusc · Answer

One  second... A circle is not a function... right?

arindameducationusc · Answer

As intersects two times along x-axis.

usukidoll · Answer

it's not a function.. fails the vertical line test