Reciprocal Function Graph: How to Determine the Equation?

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In summary, the conversation is about finding the equation of a reciprocal function given its graph with asymptotes at x=1 and x=-1. The graph has a > curve in the first quadrant and a < curve in the second quadrant, with a parabola between the asymptotes and a maximum of -1. The equation of f(x) is found to be 2x^2-1, and the reciprocal function is 1/(2x^2-1). The person is unsure if this is correct and is seeking help.
  • #1
aisha
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OK I am given the graph of a reciprocal function the asymptotes are x=1 and x=-1
Quadrants ____1____|____2_____
3 | 4

Ok in the first quadrant there is a > looking curve going through the invariant point 1 and in the second quadrant there is a < curve going through the invariant point 1. then there is a parabola with a max of -1 inbetween the asymptotes.

The question says determine the equation of the graph, so I need to find f(x) and then to get the reciprocal just put 1/(f(X)). I sketched f(x) but how do I find out the eqn? :confused:
 
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  • #2
Does it look like the [tex]f(x)=\frac{1}{4*x^2-1}[/tex] in your other thread?

If so, try a function with a similar form: [tex]f(x)=\frac{a}{bx^2-c}[/tex]
and find a,b and c by plugging in coordinates from the graph.
 
  • #3
no i graphed the equation in my other post it does not look similar to this one. I still have no idea of how to determine the equation, all I know is to find the equation of f(x) first then find 1/f(x). :cry:

Well this is what I just tried since the vertex of f(x) is 0,-1 I subbed this into the equations y=a(x+h)^2-K and then I took a point from the graph (the invariant point, 1,1) and then solved for a... a=2 so my equation for f(x) became 2x^(2)-1 that means the reciprocal must be 1/2x^(2)-1
Im not sure if this is the correct way, I tried graphing the equation using my ti 83 graphing calculator, but the reciprocal function looks different from the one on my hand out, so i can't check If I am right? What do I do? does this seem right? :cry: please HELP ME !
 
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  • #4
Please Help Me Please

:cry: No one is helping me out, I am stuck well I tried and for my graph I got the equation 1/(2x^(2)-1) . HELP PLEASE
 

1. How do you determine the equation of a line from a graph?

To determine the equation of a line from a graph, you need to identify two key pieces of information: the slope of the line and the y-intercept. The slope can be found by calculating the change in y over the change in x, often represented as "rise over run." The y-intercept is the point where the line crosses the y-axis. Once you have these two values, you can use the slope-intercept form (y = mx + b) to write the equation of the line.

2. Can you determine the equation of a non-linear graph?

Yes, you can determine the equation of a non-linear graph by using the general form of a quadratic equation (y = ax^2 + bx + c). You will need to identify three points on the graph and then use those points to solve for the coefficients a, b, and c. Alternatively, you can also use the point-slope form (y - y1 = m(x - x1)) if you know the slope and one point on the graph.

3. What if the graph does not have numerical values on the axes?

If the graph does not have numerical values on the axes, you can still determine the equation by using the slope and a point on the line. You can also use the slope-intercept form if you can estimate the y-intercept based on the graph's shape.

4. Can you determine the equation of a line without graphing it?

Yes, you can determine the equation of a line without graphing it if you know two points on the line. You can use the slope formula or the point-slope form to find the equation without needing to plot the points on a graph.

5. How can you check if the equation you determined is correct?

You can check if the equation you determined is correct by substituting in the coordinates of the points used to determine the equation. If the equation is correct, the coordinates should satisfy the equation. You can also graph the equation to see if it matches the original graph.

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