Vertical Lines of x=5 & x=0 in y=ln(x-5)/x

In summary, the vertical lines of x=5 and x=0 in the function y=ln(x-5)/x represent the values of x=5 and x=0 respectively and act as vertical asymptotes in the graph. They indicate restrictions and help in understanding the function's behavior near these points. They cannot be removed or changed as they are essential in understanding the function. They also divide the domain into three parts and affect the range of the function.
  • #1
Petrus
702
0
Hello MHB,
I did find a problem in internet
\(\displaystyle y=\frac{ln(x-5)}{x}\)
they say there is a vertical line at \(\displaystyle x=5\) but should there not also be a vertical line at \(\displaystyle x=0\)?

Regards,
\(\displaystyle |\pi\rangle\)
 
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  • #2
Petrus said:
Hello MHB,
I did find a problem in internet
\(\displaystyle y=\frac{ln(x-5)}{x}\)
they say there is a vertical line at \(\displaystyle x=5\) but should there not also be a vertical line at \(\displaystyle x=0\)?

Regards,
\(\displaystyle |\pi\rangle\)

\(\displaystyle \ln(x-5) \) is undefined at $x=0$ actually the function cannot get closer to this line.
 

FAQ: Vertical Lines of x=5 & x=0 in y=ln(x-5)/x

What are vertical lines of x=5 and x=0 in y=ln(x-5)/x?

Vertical lines of x=5 and x=0 in y=ln(x-5)/x are two vertical lines on a graph that represent the values of x=5 and x=0 respectively in the equation y=ln(x-5)/x. These lines are important in understanding the behavior of the function and its asymptotes.

How do the vertical lines of x=5 and x=0 affect the graph of y=ln(x-5)/x?

The vertical lines of x=5 and x=0 act as vertical asymptotes for the graph of y=ln(x-5)/x. This means that the function cannot be evaluated at these points and the graph will approach but never touch these lines.

What is the significance of the vertical lines of x=5 and x=0 in y=ln(x-5)/x?

The vertical lines of x=5 and x=0 in y=ln(x-5)/x are important because they indicate the restrictions of the function. They also help in understanding the behavior of the function near these points.

Can the vertical lines of x=5 and x=0 be removed or changed in the graph of y=ln(x-5)/x?

No, the vertical lines of x=5 and x=0 cannot be removed or changed in the graph of y=ln(x-5)/x as they represent the values of x=5 and x=0 respectively in the equation and are essential in understanding the behavior of the function.

How do the vertical lines of x=5 and x=0 affect the domain and range of the function y=ln(x-5)/x?

The vertical lines of x=5 and x=0 divide the domain of the function into three parts: (-∞,0), (0,5), and (5,∞). The range of the function is also affected as it cannot take on values at x=5 and x=0. The range of the function is (-∞,∞) with the exception of y=0, which is not in the range.

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