Analyze the asymptotes of the function.
y=1 / x+4
which of the following options are the equations of the function’s asymptotes? select all that apply.
x = -4
x = 4
y = -4
y = 4
x = 0
y = 0

Option 1 and 6.

The vertical asymptote is x=-4.

The horizontal asymptote is y=0.

Step-by-step explanation:

Given : Function

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.

Denominator =0

So, vertical asymptote is x=-4.

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

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.

range is infinite on both x and y axis positive and negative

step-by-step explanation:

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0