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no hold on :)

|dw:1439337786064:dw|

Do you mean \(\Large f(x)=\frac{2x^2−x−3}{x^2−2x−3}\)

yes:)

Do you know how to factorize quadratic expressions?

yes!

So I got for the first one, (x+1)(2x-3)

So factor the numerator and denominator, as a start! ok?

Got it:) So, I gottt
(x+1)(2x-3)/(x+1)(x-3)

Canceling out the x+1

Just like that, or with a condition?

I dont know what you mean by that? So, I'm going w/ "just like that."

So what are you left with?

2x-3/x-3 :)

or
\(\Large f(x)=\frac{(2x-3)}{(x-3)}, .... x\ne -1\)

What else do you see?

You can take out the x-3 and ur left with the 2

You cannot simplify further, so you have to think of graphing what's left.

Ok:)

What graphing features do you see in the simplified function?

ok hold on:)

It goes in opposite directions

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--

Well, have you learned about asymptotes?

A horizontal asymptote for this may be 2/3

Do you see a vertical asymptote?

no! Okay thats wrong! I mean 3,-3

|dw:1439339170261:dw|

What about the horizontal asymptote?

hm...I give up on that one haha! So, I'm just going to guess and say 2/1

You would divide the coefficients of x, so 2x/x=2, yes 2/1=2 is correct.

|dw:1439339327350:dw|

:) Yay! Now what about the domain and range?

We'll finish drawing the graph first.
Do you know what it looks like?

A point of intersection? Between the vertical and horizontal lines

No this graph does not intersect itself, but it runs close to the two asymptotes that i drew.

=-0.2

not really,
f(2.9)=(2*2.9-3)/(2.9-3)=2.8/(-0.1)=-28
Your turn to do the same for f(3.1)...

-32

It's +32. The denominator is +0.1.

So now we can complete the graph, remembering that \(x\ne-1\) !

|dw:1439339824439:dw|

Can you now do the domain and range?

I'll try. So y>-1 and the domain could be all real numbers except 3

How about -1 which we have shown an empty circle?

Idk:(

Right!

*-1
So what is the domain?

there would be one?

Your proposed domain was almost right, except that you missed out the -1, so...

Ok:) Thanks<3 I thought so, but I wasnt sure

So what is it?

all reals except 3,-1

Good!
Now proceed with the range, and you'd be done!

Thank goodness lol!

So what's the range?

**Silence**
Takes a wild guess and goes with...y>2/3

Look at the graph for a start!
There are two points to be excluded.

2 and 3?

We're looking at range, or the y-axis. So look for y-values that we cannot get from the graph!

On the graph? ok so -1

-1 is for x. What is the corresponding value for y????

I.e. what is f(x) as x -> -1?

i gotta go eat dinner! Thanks so much for all your help:). I'll be back in 30 minutes or so:)

I will be gone by then. Someone else should be able to continue!
Bon apetite!