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

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.