SOLUTION: f(0)=-5 and f(3)=4 A function is f(x)=?

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Question 1099748: f(0)=-5 and f(3)=4
A function is f(x)=?
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming this function is linear. If so, then we first need the slope

Slope Formula:

m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m+=+%284-%28-5%29%29%2F%283-0%29 Plug in (x1,y1) = (0,-5) and (x2,y2) = (3,4)

m+=+%284%2B5%29%2F%283-0%29

m+=+%289%29%2F%283%29

m+=+3

The slope is 3

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Use one of the points -- say (x,y) = (0,-5) -- and the slope m = 3 to find the y intercept b

y+=+mx%2Bb

-5+=+3%2A0%2Bb Plug in m = 3, x = 0, y = -5

-5+=+0%2Bb

-5+=+b

b+=+-5

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The slope is m+=+3. The y intercept is b+=+-5

Therefore y+=+mx%2Bb turns into y+=+3x%2B%28-5%29 which simplifies to y+=+3x-5

Replace y with f(x) and we have this final answer f%28x%29+=+3x-5

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)= y     f(x)=y
f(0)=-5 and f(3)=4 
 (0, -5)     (3, 4) 
So the function f(x) goes through the two points:

(x,y) = (0,-5) and (x,y) = (3,4)

Plot those two points:



f(x) could be a straight line through them, like this



That has the equation f(x) = 3x-5, which is found by substituting
the two points into the slope formula to find the slope,
and then substituting in the point-slope formula, and
simplifying.  Then when you have y = 3x-5, substitute f(x) for y.

Or it could be this function



which is f%28x%29+=+-x%5E2%2B6x-5

Or it could be this function



which is f%28x%29+=+-x%5E3%2B5x%5E2-3x-5

Or it could be any of thousands of other functions.

Edwin