Sketching the Curve (1/x2) - 1

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In summary, the graph of (1/x<sup>2</sup>) - 1 is a hyperbola with a vertical asymptote at x=0 and a horizontal asymptote at y=-1. The domain is all real numbers except 0 and the range is all real numbers greater than or equal to -1. Changing the value of x affects the steepness and orientation of the hyperbola. The important points on the graph are the vertical and horizontal asymptotes, as well as the two x-intercepts at x=1 and x=-1. This function can be used to model inverse relationships in real-world applications, such as gravitational force and reaction rate in chemistry.
  • #1
lionely
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I need to sketch the curve (1/x2) - 1

Is this correct?

2ilmse1.png



Excuse the untidiness this was drawn in paint. :S

I know the y-axis is an asymptote to the function, I haven't sketch a graph like this before so I'm kind of confused.
 
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  • #2
when x=1 then what is y? do you see that point on your graph?

similarly for x=-1

try generating several points at x=2,3,4... and plot them
 
  • #3
oh.. sigh I see a part if below the x-axis now thanks.
 

Related to Sketching the Curve (1/x2) - 1

1. What does the graph of (1/x2) - 1 look like?

The graph of (1/x2) - 1 is a hyperbola that is shifted down by 1 unit. It has a vertical asymptote at x=0 and approaches the x-axis as x gets larger or smaller.

2. What is the domain and range of the function (1/x2) - 1?

The domain of (1/x2) - 1 is all real numbers except 0, since division by 0 is undefined. The range is all real numbers greater than or equal to -1, since the function is always at or below -1.

3. How does changing the value of x affect the graph of (1/x2) - 1?

As x gets larger or smaller, the graph approaches the x-axis and becomes steeper. When x=1 or -1, the graph has a value of 0. Changing the sign of x will also change the orientation of the hyperbola.

4. Are there any important points or features on the graph of (1/x2) - 1?

The graph has a vertical asymptote at x=0 and a horizontal asymptote at y=-1. It also has two x-intercepts at x=1 and x=-1. These points are important in understanding the behavior of the graph.

5. How can this function be used in real-world applications?

The function (1/x2) - 1 can be used to model the relationship between two variables that are inversely proportional. For example, it can be used to represent the relationship between distance and strength of gravitational force, or between concentration and reaction rate in chemistry.

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