Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f (x) = x + 4 if x 1 x = (smaller value) continuous from the right continuous from the left neither

the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right, when

when x→a⁺ lim f (x) = f (a)

and from the left when

when x→a⁻ lim f (x) = f (a)

then since the functions presented are continuous, we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f (x) = lim e^x = e^0 = 1

when x→0⁻ lim f (x) = lim (x+4) = (0+4) = 4

then since f (0) = e^0=1, the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f (x) = lim (8-x) = (8-0) = 8

when x→1⁻ lim f (x) = lim e^x = e^1 = e

then since f (1) = e^1=e, the function is continuous from the left at x=1