Answer: k = 4
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Step-by-step explanation:
The piecewise function is essentially two different functions joined together. In this case,
h(x) = kx if 0 <= x < 1
OR
h(x) = x+3 if 1 <= x <= 5
The value of x determines which piece we use.
The two pieces will join together to be continuous only if the y value is the same for x = 1.
Plug x = 1 into the first piece and we get
h(x) = k*x
h(1) = k*1
h(1) = k
Do the same for the second piece
h(x) = x+3
h(1) = 1+3
h(1) = 4
Set the two results (k and 4) equal to each other and we get k = 4.