SOLUTION: Given the rational function f(x)=(12x-3)/(3x(^2)+1) Algebraically A) Find the domain. B)Find the equation of each vertical asymptote, if any. C) Find the equation of any horizonta

Question 200091: Given the rational function f(x)=(12x-3)/(3x(^2)+1) Algebraically A) Find the domain. B)Find the equation of each vertical asymptote, if any. C) Find the equation of any horizontal asymptote and explain how you found the equation. D) Find the range E) Determine symmetry F) Find any intercepts that the graph of the fuction may produce G) Algebraically find points between andbeyond each x-intercept and vertical asymptote. Please show all algebra work done to obtain answers A-F. Thanks for your help!
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a) domain is all real numbers because 3x^2 can never be -1
b) there is no vertical asymptote because the domain is all real numbers.
c)since the degree of the expression in the denominator is one more than the degree in the numerator there is a horizontal asymptote at y=0
d)range: for y is between -5.263... and 2.275... (graphing calculator)
e) the graph is asymmetric.
f) x intercept (when y=0) :
12x-3/3x^2+1=0
12x-3=0 multiply each side by 3x^2+1
12x=3
x=1/4
You can find any other points you wish.
.
Ed
.

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