Please Help,
Create a rational function with a linear binomial in both the numerator and denominator.

Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.

Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.

Question

Please Help, 
Create a rational function with a linear binomial in both the numerator and denominator.

Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.

Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.

anonymous · Answer

Rational function looks like a fraction.  Linear binomial is something like (x-2).  You want similar terms in both the numerator and the denominator, so it might look like$$f(x)=\frac{x-a}{x-b}$$Pick numbers for a and b, and you are on your way.

anonymous · Answer

does it matter which numbers I pick

anonymous · Answer

Nope, as long as they aren't zero, or the same as one another.

anonymous · Answer

ok so a=3 b=5

anonymous · Answer

I recommend easy numbers: small integers.

anonymous · Answer

Yeah, that will work.

anonymous · Answer

ok so I would just graph those and then how would I figure out part 2

anonymous · Answer

Well, the vertical asymptote is at the undefined value of x.  Can you tell me what that is?

anonymous · Answer

im not really sure im like confused

anonymous · Answer

Well, is there any number that is excluded from the domain?

anonymous · Answer

We aren't allowed to divide by zero, so any number that makes the denominator of the function zero can't be in the domain.  What value of x would that be?

anonymous · Answer

um im not really sure would it be like 5

anonymous · Answer

Exactly.  That means x=5 is the vertical asymptote.  Now, how do we find the x intercept?

anonymous · Answer

If the function is intercepting the x axis, what is the y value?

anonymous · Answer

ok well I graphed $$f(x)=\frac{ x-3 }{ x-5 }$$ and got 3 as the x intercept

anonymous · Answer

Correct.  To do it algebraically, you set y (keeping in mind that y = f(x)) to be zero.  That will allow you to get that solution.  Good.  Two down, one to go.  How do we find the y intercept?

anonymous · Answer

do you set x=0

anonymous · Answer

Yep.

anonymous · Answer

so would the y intercept be 0.6

anonymous · Answer

Looks like you've got it.  Nice work.  Do math every day.

anonymous · Answer

lol thank you so much this really helped me a lot

anonymous · Answer

No sweat.  Do math every day.