SOLUTION: Stan is so good i had to come back for more. 1)Given the function y=2x-3/x-1 what are the a)x intercept b)y intercept c)vertical asymptote(s) d)horizontal asymptote(s)

Algebra.Com
Question 156953: Stan is so good i had to come back for more.
1)Given the function y=2x-3/x-1 what are the
a)x intercept
b)y intercept
c)vertical asymptote(s)
d)horizontal asymptote(s)
e)slant asymptote
2)For the function f(x)=x^2(x-2)
a)find the X intercepts and for each intercept indicate whether the graph of F crosses (c) or merely touches (t)the X axis at each intercept.
b)find the Y intercept
c)Over what interval is f>0?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you going in the right direction


1)

a) x intercept


The x-intercept occurs when .


Start with the given equation


Plug in


Multiply both sides by


Multiply 0 and to get 0


Add 3 to both sides.


Divide both sides by 2


So the answer is which means that the x-intercept is , which is (1.5, 0). Note: the x-intercept is in the form of (x, 0)


------------------------------------

b)y intercept


The y-intercept occurs when



Start with the given equation


Plug in


Multiply


Subtract


Reduce


So the answer is which means that the y-intercept is Note: the y-intercept is in the form of (0, y)


----------------------------------------

c)vertical asymptote(s)


To find the vertical asymptote, just set the denominator equal to zero and solve for x (remember you CANNOT divide by zero)


Set the denominator equal to zero


Add 1 to both sides


Combine like terms on the right side


So the vertical asymptote is


-------------------------------------------


d)horizontal asymptote(s)


Since the degree of the numerator and the denominator are the same, we can find the horizontal asymptote using this procedure:

To find the horizontal asymptote, first we need to find the leading coefficients of the numerator and the denominator.

Looking at the numerator , the leading coefficient is

Looking at the denominator , the leading coefficient is

So the horizontal asymptote is the ratio of the leading coefficients. In other words, simply divide by to get


So the horizontal asymptote is


-------------------------------------------------

e) slant asymptote

Since horizontal asymptote exists, there isn't a slant asymptote (you either have one or the other, but not both)


--------------------------------------------------



Notice if we graph , we can visually verify our answers:


Photobucket - Video and Image Hosting
Graph of with the x-intercept (or the point (1.5, 0)), the y-intercept (0,3), the horizontal asymptote (blue line) and the vertical asymptote (green line)



--------------------------------------------------


With this info, you should have a better understanding on how to approach # 2. If you're still having trouble with # 2, then repost the question.
RELATED QUESTIONS

Thanks for any help! I'm not good in algebra and need to pass to grad. I will have more... (answered by Aldorozos)
Tomorrow I have a test on slope intercept form, and solving system of equation. For slope (answered by stanbon)
1)Given the function y=x+2/2x^2-4 what are the a)x intercept b)y intercept... (answered by lwsshak3)
Given the function 2x+y=7 find the following: a. X-intercept b. Y-intercept c. Slope... (answered by ewatrrr)
Doing algebra and these 3 questions have me stuck, I've tried several times. It's hard to (answered by solver91311)
Find the y-intercept and the x-intercept for the equation. -6x+y=22 What is the... (answered by Alan3354)
What is the f(x) = mx + b, given the x- and y-intercept of the linear function.... (answered by josgarithmetic)
Answer the question about the given function. Given the function f(x) = -2x^2 + 4x + 3, (answered by josgarithmetic)
what is the slope intercept form for the line x intercept 3, y intercept... (answered by lwsshak3)