Question

The graph of the function has a vertical asymptote of x =

The graph of the function has a horizontal asymptote of y =
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Answer 1

The correct answers are:
(1) The graph of the function has a vertical asymptote of x = 0
(2) The graph of the function has a horizontal asymptote of y = 0

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

Rational Function = f(x) = $\frac{1}{x}$

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 = f(x) = $\frac{1}{x}$

We can write it as:

f(x) = $\frac{1 * x^0}{x^1}$

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

Answer 2

The graph of the function has a vertical asymptote of x = 0.

The graph of the function has a horizontal asymptote of y = 0.

Given :

Function -  $f(x)=\dfrac{1}{x}$

Solution :

• Line that approaches a curve is known as asymptote, as it heads towards infinity.
• Types of assymptote - horizontal, vertical and oblique.

To find the vertical assymptote, put the denominator equals to zero as follows:

$f(x)=\dfrac{1}{x}$

Denominator = x = 0.

Therefore vertical assymptote is x = 0.

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

$f(x) =\dfrac{1}{x}$

$f(x) = \dfrac{1\times x^0}{x^1}$

We know that the power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y = 0.

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

For more information, refer the link given below

https://brainly.com/question/23283241