Hyperbola graphing?

[Rose34]

How to graph the hyperbola of y=1/x-1?

Normally when it is like y=-1/2x+5 I know how to graph it but when the last value(5 or any number) is missing I do not know how to graph it

Thanks in advance!

[Ionic Doc]

How to graph the hyperbola of y=1/x-1?

Normally when it is like y=-1/2x+5 I know how to graph it but when the last value(5 or any number) is missing I do not know how to graph it

Thanks in advance!

Hey Rose,

x-1   simply means a horizontal shift on the x-axis to the right by 1 unit.
You usually equate the bottom part of the fraction to 0 and solve for x, to find the vertical asymptote.
So your vertical asymptote will be at x=1

For your other example of y=-1/2x+5
Your vertical asymptote will be at

2x+5=0
Therefore x= -5/2

Back to your original question, of y=1/x-1
The horizontal asymptote would be 0.

Edit: Forgot to mention, if you want to find your y-intercept, then let x=0
So y=1/0-1
y = -1
Therfore your y-intercept is (0,-1)

For your x-intercept you let y=0.
Therefore in this graph, there  is no x-intercept

Knowing this you can graph your hyperbola, it should look something like:

(make sure your hyperbolae never touch the vertical and horizontal asymptotes)

I hope this helped, also use this website called desmos to play around with graphs and see what they would look like, it really helps (here's the link:  https://www.desmos.com/calculator     

[Rose34]

Hey Rose,

x-1   simply means a horizontal shift on the x-axis to the right by 1 unit.
You usually equate the bottom part of the fraction to 0 and solve for x, to find the vertical asymptote.
So your vertical asymptote will be at x=1

For your other example of y=-1/2x+5
Your vertical asymptote will be at

2x+5=0
Therefore x= -5/2

Back to your original question, of y=1/x-1
The horizontal asymptote would be 0.

Knowing this you can graph your hyperbola, it should look something like:
(Image removed from quote.)
(make sure your hyperbolae never touch the vertical and horizontal asymptotes)

I hope this helped, also use this website called desmos to play around with graphs and see what they would look like, it really helps (here's the link:  https://www.desmos.com/calculator   

Thank you very much!!