The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0

Explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.

Rational Function = g(x) = $\frac{10}{x}$ 

Denominator = x = 0

Hence the vertical asymptote is x = 0.

(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:

Given function = g(x) = $\frac{10}{x}$ 

We can write it as:

g(x) = $\frac{10 * x^0}{x^1}$ 

If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.

In above case, 0 < 1, therefore, the horizontal asymptote is y = 0

5 0

3 years ago

Read 2 more answers