SOLUTION: Help with rational functions these are confusing me: y = 3(2^x)-1 r(x) = ((2x+1)x)/(4-x^2) How would I get the vertical/horizontal asymptotes along with the x and y

Question 912332: Help with rational functions
these are confusing me:
y = 3(2^x)-1
r(x) = ((2x+1)x)/(4-x^2)

How would I get the vertical/horizontal asymptotes along with the x and y intercepts from these rational functions?
Please explain
Thank you
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The first equation or function is not a rational one, but is a polynomial equation or function. The function r(x) IS a rational function. You need to learn what is a polynomial function and then what is a rational function before you can effectively make the sense of these in the way that you are asking. They ARE related but they are not the same thing.

Moving directly to the r(x), the RATIONAL function,
when factored.

No factor common to both numerator and denominator, meaning no holes.

Undefined for x at 2 and -2, so r(x) has vertical asymptote at x=-2 and at x=2.

x-intercepts for x=0 because it is a factor in the numerator, and for x=-1/2 which makes the binomial 2x+1=0; so x-intercepts and .

y-intercept: Let x=0, and evaluate r(0).
RELATED QUESTIONS
How to get the x- and y-intercept and the horizontal and vertical asymptote(s) of these... (answered by josgarithmetic)

Please help me with these two questions I dont understand and they are very confusing.... (answered by solver91311)

I need help with graphing rational funtions. The question is...Identify the points of... (answered by stanbon)

What would be the equations of the vertical asymptote(s) and horizontal asymptotes of... (answered by lwsshak3)

Please help me with the following three questions they are very confusing and i don't... (answered by checkley71)

Which one of these are functions? 1) x = 4 2) y = 2x + 5 3)... (answered by oscargut)

I Dont Understand How Do Do These Problems: It Says I have to identify any holes or... (answered by stanbon)

how to solve the x- and y- and asymptotes of these rational functions?... (answered by josgarithmetic)

Use the equation and type the ordered-pairs. 1) y=3^x 2) y = 10^x 3) y=(1/2)^x (answered by richard1234)