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

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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) About Me  (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,
r%28x%29=%28x%282x%2B1%29%29%2F%28%282-x%29%282%2Bx%29%29 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 x=-1%2F2 and x=0.

y-intercept: Let x=0, and evaluate r(0).