Find x Value for Cubic Function with TI-83

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Discussion Overview

The discussion revolves around finding the x value for a given y value in a cubic function using a TI-83 calculator. Participants explore various methods and functionalities of the calculator related to graphing and solving equations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests plotting both the cubic function and a constant function to find the intersection point, which represents the x value for a given y value.
  • Another participant expresses confusion about the intersect function and its prompts, particularly when dealing with large y values, leading to an error message.
  • Some participants clarify that the "Value" option in the Calc menu can be used to find y values for given x values, but this does not directly address the original question of finding x for a given y.
  • One participant states that there is no straightforward method on the TI-83 to find x for a given y due to the possibility of multiple x values corresponding to a single y value in a cubic function.
  • Another participant proposes solving the equation f(x) - k = 0, suggesting either plotting f(x) - k to find x-intercepts or using the intersection of f(x) and k to find the x-coordinate where they meet.
  • A later reply indicates that the proposed method of plotting f(x) - k worked for them, suggesting it as a viable approach.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to find the x value for a given y value. Multiple competing views and methods are presented, with some participants expressing confusion and others providing alternative solutions.

Contextual Notes

Participants mention limitations related to the TI-83's capabilities, particularly regarding the handling of multiple x values for a single y value in cubic functions. There are also references to specific calculator functions that may not be universally understood or remembered.

cscott
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With my buddies TI-83 I've plotted a cubic function but am wondering how I can find the x value for a given y value.
 
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Plot both f(x), the cubic, and g(x)=k, the constant function.

On top of "Trace", click on "Calc."

Go through the menu, look for intersect, and follow the instructions.

(The menu titles might not be exact, I don't have one in front of me)
 
I'm not sure if I totally follow but I assumed k = "y value". In my case this was 10^12. I don't really know what the intersect function is asking by "first curve?", "second curve?" and "guess?", but I clicked past them. With lower numbers it seems to work but with 10^12 I get "ERR: NO SIGN CHNG"
 
While viewing the graph, click "2nd" then "Trace" to bring up the Calc menu. Select "Value" and enter the x value for which you want the y value. You don't use "Intersection" unless you want the point at which two or more curves intersect and from what you're saying there's only one curve.
 
z-component said:
While viewing the graph, click "2nd" then "Trace" to bring up the Calc menu. Select "Value" and enter the x value for which you want the y value. You don't use "Intersection" unless you want the point at which two or more curves intersect and from what you're saying there's only one curve.

I want to do the opposite of what you described! I need the x value for a given y value. Thanks anyway.
 
Last edited:
Oh, there is no way that I know of using the original graphing software on the TI-83 to do that. I suppose the reason is because there can be multiple x values for a single y value in a function, not the other way around.
 
sure he can, simply by doing it my way...

Basically, he wants to solve for f(x)-k=0. So he can either plot f(x)-k, and look for where it crosses the x-axis (I don't remember if a function does that), or make two curves, f(x) and k, and find the x-coordinate of their intersection. Their intersection is where f(x)=k.

Another way would be to go into the solver (i don't remember where it is to be honest, hopefully you know...), which solves equations for you.
 
tmc said:
sure he can, simply by doing it my way...

Basically, he wants to solve for f(x)-k=0. So he can either plot f(x)-k, and look for where it crosses the x-axis (I don't remember if a function does that), or make two curves, f(x) and k, and find the x-coordinate of their intersection. Their intersection is where f(x)=k.

Another way would be to go into the solver (i don't remember where it is to be honest, hopefully you know...), which solves equations for you.

Yes, this worked. Thanks!
 
tmc said:
sure he can, simply by doing it my way...

Basically, he wants to solve for f(x)-k=0. So he can either plot f(x)-k, and look for where it crosses the x-axis (I don't remember if a function does that), or make two curves, f(x) and k, and find the x-coordinate of their intersection. Their intersection is where f(x)=k.

Another way would be to go into the solver (i don't remember where it is to be honest, hopefully you know...), which solves equations for you.
I understand where you're coming from now. That's a nice skill. I'll have to try that out sometime. :)
 

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