text: # Thread: Finding formula for a function
  
  1. ## Finding formula for a function
  
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  
  2. Originally Posted by JAMESveeder
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  We can model the function using a linear equation.
  
  Note that when x increases by 2, f(x) increases by 28.72
  
  Since $f(0)=3.5=b$ and the slope of the line is $m=\frac{28.72}{2}=14.36$, it follows that the equation of the line is $f(x)=mx+b=14.36x+3.50$.
  
  3. Originally Posted by JAMESveeder
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  Try plotting it!
  
  It's a straight line passing through (0,3.5) and with slope 14.36
  
  CB
  
  4. Great explanation, thank you!
  
  You can't use the same method for an exponential function though, can you?
  
  5. Originally Posted by JAMESveeder
  Great explanation, thank you!
  
  You can't use the same method for an exponential function though, can you?
  No. For an exponential function, you would need to find a common RATIO. In other words, you need to find what each number is MULTIPLIED by to get the next.
  
  6. So with this:
  Code:
  x      g(x)
  .5     -1
  1       0
  2       1
  4       1
  8       3
  Each number is multiplied by 2
  
  So how would I apply that to the explanation that was said before?
  
  7. Originally Posted by JAMESveeder
  So with this:
  Code:
  x      g(x)
  .5     -1
  1       0
  2       1
  4       2
  8       3
  Each number is multiplied by 2
  
  So how would I apply that to the explanation that was said before?
  you would find the line through the data: $x,\ \log_2(g(x))$ .. or on second thoughts $\log_2(x),\ g(x)$
  
  CB
  
  8. Ah, thanks CaptainBlack
  
  This helps a lot, thanks very much guys.
explanation: The document is a thread from a forum where a user is seeking help to find the formula for a given function based on a set of data points. The thread contains a question and multiple responses providing explanations and methods to solve the problem. The user also asks a follow-up question about applying the method to an exponential function, and receives further guidance.
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distilabel_metadata.role: system
distilabel_metadata.content: # Thread: Finding formula for a function
  
  1. ## Finding formula for a function
  
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  
  2. Originally Posted by JAMESveeder
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  We can model the function using a linear equation.
  
  Note that when x increases by 2, f(x) increases by 28.72
  
  Since $f(0)=3.5=b$ and the slope of the line is $m=\frac{28.72}{2}=14.36$, it follows that the equation of the line is $f(x)=mx+b=14.36x+3.50$.
  
  3. Originally Posted by JAMESveeder
  I need to find the formula for this function, and i'm not sure what to do...
  
  Code:
  x     f(x)
  -2    -25.22
  0      3.50
  2      32.22
  4      60.94
  6      89.66
  I've looked all over the internet and can't find anything to help me out
  Try plotting it!
  
  It's a straight line passing through (0,3.5) and with slope 14.36
  
  CB
  
  4. Great explanation, thank you!
  
  You can't use the same method for an exponential function though, can you?
  
  5. Originally Posted by JAMESveeder
  Great explanation, thank you!
  
  You can't use the same method for an exponential function though, can you?
  No. For an exponential function, you would need to find a common RATIO. In other words, you need to find what each number is MULTIPLIED by to get the next.
  
  6. So with this:
  Code:
  x      g(x)
  .5     -1
  1       0
  2       1
  4       1
  8       3
  Each number is multiplied by 2
  
  So how would I apply that to the explanation that was said before?
  
  7. Originally Posted by JAMESveeder
  So with this:
  Code:
  x      g(x)
  .5     -1
  1       0
  2       1
  4       2
  8       3
  Each number is multiplied by 2
  
  So how would I apply that to the explanation that was said before?
  you would find the line through the data: $x,\ \log_2(g(x))$ .. or on second thoughts $\log_2(x),\ g(x)$
  
  CB
  
  8. Ah, thanks CaptainBlack
  
  This helps a lot, thanks very much guys.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a thread from a forum where a user is seeking help to find the formula for a given function based on a set of data points. The thread contains a question and multiple responses providing explanations and methods to solve the problem. The user also asks a follow-up question about applying the method to an exponential function, and receives further guidance.
  
  Label: question-and-answer