Response:
This function is continuous from the left at x=1 and from the right at x=0.
Detailed Explanation:
A function is said to be continuous from the right at a point if:
when x→a⁺ lim f(x)=f(a)
And continuous from the left if:
when x→a⁻ lim f(x)=f(a)
Thus, as the functions presented are continuous, we must search for points of discontinuity only when the functions transition.
At 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
Therefore, since f(0) = e^0=1, the function is continuous from the right at x=0.
At 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
Hence, since f(1) = e^1=e, the function is continuous from the left at x=1.
