Write the function f(x) that satisfies f(2)=5 and f(3)=8

Answer 1

f(2) = 5, f(3) = 8 describes two points (2,5) and (3,8). Plot them and draw a straight line through them.

that line's equation is y=3x-1

f(x) = 3x-1

a linear function, with slope=3 and y intercept=-1

slope = (8-5)/(3-2) = 3/1 = 3

use either point to get the equation (y-8)/(x-3) = 3

y-8 = 3x-9

y =3x -9 +8 = 3x -1

or use (2,5)

y-5 = 3(x-2) = 3x -6

y=3x-6+5 = 3x-1

y= f(x) = 3x-1

There are also quadratic or higher order equations that go through those same two points.