Question

Is it possible to have a function f that satisfies the following conditions?

(1) The domain of f (x) is [ -5, 5].
(2) f (-5) = f ( -4 ) = 2 ; f ( 4 ) = f (5) = 1.
(3) f has an infinite discontinuity at -4 and a jump discontinuity at 4.
(4) f is left continuous at -4 and right continuous at 4.

Answer 1

It will be a piecewise function....

x less than or equal to -4, f(x) = 2
x greater than or equal to 4, f(x) = 1
In between, the function will be a rational function that has (x+4) in the denominator plus something that makes it jump to 1 when x=4.

Answer 2

It will be a piecewise function....

x less than or equal to -4, f(x) = 2
x greater than or equal to 4, f(x) = 1
In between, the function will be a rational function that has (x+4) in the denominator plus something that makes it jump to 1 when x=4.

Answer 3

thanks!