Question

what is the vertical asymptote of y=1/x-5

Answer 1

When you graph it. You have to look at the line at which it approaches. It approaches x = 0 when graphed.

Answer 2

The mathematical way to find the vertical asymptote is to set the denominator equal to zero, then solve for x.

Your problem does not have like denominators so, start getting like terms on the denominator first.
\[y =\frac{ 1 }{ x } - 5 = \frac{ 1 }{ x } - \frac{ 5x }{ x } = \frac{ 1-5x }{ x }\]
so your new equation is
\[y = \frac{ 1-5x }{ x }\]

Answer 3

As you can see, the denominator is x. Setting x equal to zero leaves no further work to be done. It is simply x = 0. That is your vertical asymptote.

Answer 4

the vertical asymptote is 5 because you set x-5=0

Answer 5

@michhellelynn

Use grouping symbols to clarify the problem.

Is this --> y=1/x-5

supposed to be y = (1/x) - 5 OR y = 1/(x - 5) ?

Answer 6

According to the way she wrote it: y = 1/x-5, using PEMDAS rule, it is y = (1/x) - 5.

Answer 7

\[y=\frac{ 1 }{ x-5 }\]
this is how I interpret this, since there are no parenthesis. you don't typically see rational function problems like
\[y=\frac{ 1 }{ x }-5\]