Question

Analyze the asymptotes of the function.

Answer 1

Answer:

Option 1 and 6.

The vertical asymptote is x=-4.

The horizontal asymptote is y=0.

Step-by-step explanation:

Given : Function $y=\frac{1}{x+4}$

To find : Analyze the asymptotes of the function?

Solution :

Asymptote is a line that the graph of a function approaches but never touches.

To find the vertical asymptote put the denominator equal to zero and find the value of x.

$y=\frac{1}{x+4}$

Denominator =0

$x+4=0$

$x=-4$

So, vertical asymptote is x=-4.

Now, to find the horizontal asymptote we see the degree of both numerator and denominator.

$y=\frac{1}{x+4}$

Degree of numerator is 0

Degree of Denominator = 1

We know, When the degree of numerator is less than the degree of denominator then the horizontal asymptote is y=0.

Therefore, From the given options, Option 1 and 6 is correct.

The vertical asymptote is x=-4.

The horizontal asymptote is y=0.

Answer 2

The asymptotes will be the values for x and y that cannot exist. With fractions, you can never have a zero denominator, so solving for: x+4=0
says that x cannot be -4. That line x =-4 is a vertical asymptote where the function cannot cross.

Then you look at y, rearrange the equation.
y = 1/(x+4)
y(x+4) = 1
(x+4) = 1/y

now you can see y can never be zero. The line y = 0 is a vertical asymptote that the function will never cross over, only approach.