Answer: Yes, the function is continuous.
Step-by-step explanation:
Continuity is defined by the lim f(x) = f(a).
In this case, the piecewise function splits at x=-2, so we need to check the limit from both the left and right at x=-2.
Lim (x-2) as x approaches -2 from the left = (-2)-2=-4
Lim (3x+2) as x approaches -2 from the right is 3(-2)+2=-6+2=-4
Therefore, it is continuous
To find the limits, just plug in the number x is approaching into each function you are taking the limit of. Since x-2 is the function to the left of x=-2, plug in -2 for x when the limit is approaching x=-2 from the left. Since 3x+2 is the function to the right of x=-2, plug in -2 for x when the limit is approaching x=-2 from the right.
Basically, just check that both parts of the piecewise function give you the same answer when you plug in x=-2.
Hope this helps!!!
