# 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.
The text passage contains a series of posts 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 posts include a question, an answer, and further discussion on how to approach similar problems.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
user
The text passage contains a series of posts 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 posts include a question, an answer, and further discussion on how to approach similar problems.

TYPE: SINGLE_QUESTION_WITH_ANSWER