Question

How do you find the range of the function f(x)=x^2+x-2 divided by x^2-3x-4?

The domain is x does not equal -1 or 4.

Answer 1

@amistre64 @ganeshie8

Answer 2

The easiest way is to graph it and look at what values are not included. If it is one-to-one then you can take the inverse and find the domain of the inverse. Sometimes finding the inverse is not possible, so try the graph!

Answer 3

I don't think it is one-to-one..

Answer 4

can you graph it?

Answer 5

Yeah, I did on my calculator.

Answer 6

So what Y values are excluded?

Answer 7

When x=3, it says that the y value is ERROR.

Answer 8

But that doesn't tell me the range. I need to know how to find the range.

Answer 9

@amistre64 help pleasee :)

Answer 10

hmm, there are a few ways to view this; what level math are you studying?

Answer 11

pre-calculus.

Answer 12

\[f(x)=\frac{x^2+x-2}{ x^2-3x-4}\]
can you factor the top and bottom? if we can see the factorization we can determine certain values

Answer 13

(x+2)(x-1) is the top.

Answer 14

good, and the bottom looks to be -4 and 1

Answer 15

\[f(x)=\frac{(x+2)(x-1)}{(x-4)(x+1)}\]
we do not have any common factors top to bottom that we can cancel, so we need to see how this function is acting around x=4 and x=-1

Answer 16

function equals zero when the top is zero; at x=-2 and x=1, so lets add those to the line

Answer 17

now its a matter of determine the signage within the intervals to see how they act

Answer 18

What does that mean?

Answer 19

lets test when x = -10
\[f(x)=\frac{\cancel{(x+2)}^-\cancel{(x-1)}^-}{\cancel{(x-4)}^-\cancel{(x+1)}^1}=(+)\]
lets test when is say x = -1.5
\[f(x)=\frac{\cancel{(x+2)}^+\cancel{(x-1)}^-}{\cancel{(x-4)}^-\cancel{(x+1)}^-}=(-)

and continue this process testing a point that is within each interval

Answer 20

lol; latex fail !!

Answer 21

\[f(x)=\frac{\cancel{(x+2)}^-\cancel{(x-1)}^-}{\cancel{(x-4)}^-\cancel{(x+1)}^1}=(+)\]
\[f(x)=\frac{\cancel{(x+2)}^+\cancel{(x-1)}^-}{\cancel{(x-4)}^-\cancel{(x+1)}^-}=(-)\]

Answer 22

Haha, I'm like whaaaaaaaaaaaaaat? But, do I choose any numbers between -1 & 4?

Answer 23

And if they equal zero.. is that my range?

Answer 24

the next interval would be between -1 and 1, simplest trial is x=0 for that interval

the range is determined after the setup is completed

the next interval is between 1 and 4, use any value between 1 and 4

and for the last interval, and value greater than 4

Answer 25

I don't understand :( I'm sorry.

Answer 26

it ive done it right, i get a setup of