Question

Very urgent!
Show all work to identify the asymptotes and zero of the function:
f(x) = $\frac{5x}{x^{2}-25 }$

Answer 1

(x+1)=0

is undefined when

f(x)

giving us the vertical asymptote of

lim x→∞f(x)→∞

lim x→−∞f(x)→−∞

and

so there is no horizontal asymptote.

Since the degree of the numerator is greater than the degree of the denominator,

we can divide the denominator into the numerator to get a slant asysmptote:

f(x)=(2x2+x+2)÷(x+1)=(2x−1) +3 x+1

f(x)=2x−1

So the slant asymptote is

Answer 2

Answer:

(x+1)=0

is undefined when

f(x)

giving us the vertical asymptote of

lim x→∞f(x)→∞

lim x→−∞f(x)→−∞

and

so there is no horizontal asymptote.

Since the degree of the numerator is greater than the degree of the denominator,

we can divide the denominator into the numerator to get a slant asysmptote:

f(x)=(2x2+x+2)÷(x+1)=(2x−1) +3 x+1

f(x)=2x−1

So the slant asymptote is