f(x)=x^2/1+0.25x^2
a) find the domain of f
b) find any horizontal or vertical asymptotes

Question

f(x)=x^2/1+0.25x^2
a) find the domain of f
b) find any horizontal or vertical asymptotes

anonymous · Answer

Show the function as I think it was intended, as opposed to what you typed in:$$f(x)=x^2/(1+0.25x^2)=x^2/(1+x^2/4)$$

a)  The domain of f is all the numbers that can be successfully put in for x.  Usually, we delete those numbers that create a zero in the denominator, but there is no such real number, so$$dom(f)=\mathbb{R}=(-\infty,\infty)$$

b)Vertical asymptotes occur when the denominator goes to zero.  As discussed above, there is no such value of x, so no vertical asymptotes.  Horizontal asymptotes happen as x gets really positive or negative, and the degree of the numerator and denominator are the same.  That is not the case here, so  there are no horizontal asymptotes, either.