Provided that f(2)=24, f(-3)= -89, how to find out f(x) or the equation?

Question

Given
f(2)=24
f(-3)= -89
then, what is f(x)?

Answer 1

IF YOU KNOW IT'S LINEAR... (this doesn't work unless you know for sure the function is linear!!)

You have two points (2, 24) and (-3, -89).

Find the slope:
m = (-89 - 24) / (-3 - 2) = -113 / -5 = 113/5

Now use one point and the slope in point slope form:

y - y1 = m (x - x1)
y - (24) = (113/5)(x + 2)
y - 24 = (113/5)x + (226/5)
5y - 120 = 113x + 226
5y = 113x + 346
y = (113/5)x + (346/5)
f(x) = (113/5)x + (346/5)

Answer 2

There's no way you can tell given the information. The function could be any shape whatsoever.

If you graph the two points, they are at (-3,-89) and (2,24). The function could be any of an innumerable lines (or even 2D shapes) between, beyond, and or around them.

It could even be just discrete points if the function does not operate continuously (i.e. only for integers).

If you knew it was a straight line however, you could get the function.

Answer 3

Insufficient information. You can connect two points infinitely many ways. The shortest possible path connecting the two points is the straight line.