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All you do is plug in x = whatever wherever you see an x. So, for f(1) you are doing it for x = 1. So, plug in 1 everywhere you see an x: \[(3(1)^2-4(1)+1)/(3(1)-1)=(3-4+1)/(3-1)=0/2=0\]
You still here?
yeah im still here
That's a pretty impressive question! Here's where we start... Let's see if the top can factor first...
would i start by canceling out the 3 on the top and bottom?
No, you can't cancel them because they are not factors. You want to factor first and then cancel things.
The reason you can't cancel like that is similar to the reason you can't do this: |dw:1332645826666:dw|
You want to factor the top first... I'll show you...
lol ok i understand that concept better
Take a look at this: |dw:1332645962032:dw|
What would cancel?
Exactly! So you're left with x-1
More specifically, you're left with : f(x)=x-1
Now, let's take a look at f(1), f(0), and f(-1)
ok does this mean i already found f(-1) ?
No, that's function notation. It's just a coincidence that our function simplified down to something that has an x and a -1 in it. Here are the three things you want to simplify so you can see if they match what they question suggested they would match. f(1)=(1)-0 f(0)=(0)-1 f(-1)=(-1)-1
so how would i solve this question?
Technically, this question isn't asking you to solve anything. It's asking you to reason through and explain why certain input values cause certain output values. The three questions I posed above, what would the right side of the equal sign simplify down to? f(1)=? f(0)=? f(-1)=?
Woah - wait a sec... I typed the wrong thing
so then why would f(-1)=-1?
wouldnt it be a positive 1?
f(x)=x-1 f(1)=1-1 f(1)=0
I'm sorry about that. Let's try it again... f(x) = x-1 f(1) = 1-1 f(1) = 0 f(0) = 0-1 f(0) = -1 f(-1)=-1-1 f(-1)=-2
That's better! :)
in order for me to get this question right, what would i write? because im confused on what to say
I'm just gonna cut to the chase here: Here's how I would respond to this question... If you start by factoring this function, and simplify it, you can see that f(-1)=-2, f(0)=-1, and f(1)=0. However, because this is a rational function, we have to check its domain. If you set the original denominator to zero and solve, you see that a -1/3 should not be in the domain because it causes the function to be undefined.
Yikes, that should be a +1/3
Man, I really botched this one... lol I sure hope you're not more confused than when you started. :)
lol thank you
Sure thing! :)