Question

find k so the following function is continuous on any interval:
t + k (t is less than or equal to 12)
kt (t is greater than 12)

how can I find k?

Answer 1

here's a blank xy axis

Answer 2

now I'm going to plot the value of 12 on the x axis

Answer 3

on the left side of x = 12, we have the function t + k

t is the variable, k is some fixed number

so let's say k = -2, we'll have something like this



notice the closed circle at the endpoint

Answer 4

then to the right of x = 12, we have the function tk

since k = -2, we have y = -2t

this is only graphed when x > 12



notice the open circle