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)   (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:



Plug in (x1,y1) = (0,-5) and (x2,y2) = (3,4)







The slope is 3

------------------------------------------------

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



Plug in m = 3, x = 0, y = -5







------------------------------------------------

The slope is . The y intercept is

Therefore turns into which simplifies to

Replace y with f(x) and we have this final answer

Answer by Edwin McCravy(20055)   (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 

Or it could be this function



which is 

Or it could be any of thousands of other functions.

Edwin

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