What Does the Graph of y=(x+1)/(x-1) Look Like?

  • Thread starter brandon26
  • Start date
  • Tags
    Graph
In summary, the graph for y=(x+1)/(x-1) is a hyperbola with two branches that open in opposite directions. It is symmetrical about the lines x=1 and x=-1. The x-intercept is (1,0) and the y-intercept is (0,-1). There are two asymptotes, a vertical asymptote at x=1 and a horizontal asymptote at y=1. The domain is all real numbers except x=1 and the range is all real numbers except y=1. Changing the value of x will shift the graph horizontally and vertically, and the graph will approach the asymptotes as x approaches 1.
  • #1
brandon26
107
0
Could anyone show me what the graph of y=(x+1)/(x-1) looks like?
 
Physics news on Phys.org
  • #2
This should help:
[tex]y=\frac{x+1}{x-1}[/tex]
[tex]=\frac{(x-1)+2}{x-1}[/tex]
[tex]=\frac{x-1}{x-1}+\frac{2}{x-1}[/tex]
[tex]=1+\frac{2}{x-1}[/tex]
So it is the graph of y=1/x, just multiplied by two, shifted up by one, and shifted to the left by one.
 
  • #3
Where does the +2 come from?
 
Last edited:
  • #4
[tex]x+1=x-1+1+1=(x-1)+2[/tex]
 
  • #5
oh right. Hehe, thanks.
 
  • #6
How would simplify y=(1+2x)/(1-x)
 

1. What is the shape of the graph for y=(x+1)/(x-1)?

The graph for y=(x+1)/(x-1) is a hyperbola, which is a type of curve with two branches that open in opposite directions. It is symmetrical about the line x=1 and x=-1.

2. What are the x and y intercepts of the graph for y=(x+1)/(x-1)?

The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. For y=(x+1)/(x-1), the x-intercept is (1,0) and the y-intercept is (0,-1).

3. Are there any asymptotes in the graph for y=(x+1)/(x-1)?

Yes, there are two asymptotes in the graph for y=(x+1)/(x-1): a vertical asymptote at x=1 and a horizontal asymptote at y=1. These asymptotes occur because the function is undefined at x=1 and approaches infinity as x approaches 1, and the function approaches 1 as x approaches infinity.

4. What is the domain and range of the graph for y=(x+1)/(x-1)?

The domain of y=(x+1)/(x-1) is all real numbers except x=1, since the function is undefined at that point. The range is also all real numbers except y=1, since the function approaches that value but never reaches it.

5. How does changing the value of x affect the graph for y=(x+1)/(x-1)?

Changing the value of x will shift the graph horizontally and vertically. For example, if x is increased, the graph will shift to the left, and if x is decreased, the graph will shift to the right. Additionally, the graph will approach the asymptotes as x approaches 1.

Similar threads

  • Introductory Physics Homework Help
Replies
10
Views
678
  • Introductory Physics Homework Help
Replies
5
Views
769
  • Introductory Physics Homework Help
Replies
8
Views
557
  • Introductory Physics Homework Help
Replies
4
Views
720
  • Introductory Physics Homework Help
Replies
25
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
543
  • Introductory Physics Homework Help
Replies
2
Views
910
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
3K
Back
Top