We have been given graph of a piece-wise function. We are asked to find the limit of function as x approaches [tex]-3[/tex].
We can see that our given function has a jump discontinuity at [tex]x=3[/tex], while our function is continuous at [tex]x=-3[/tex].
We can see that the equation of line is [tex]y=1[/tex] from negative infinity to [tex]x=3[/tex].
The limit of f(x) as x approaches [tex]-3[/tex] from left side is 1 and limit of f(x) as x approaches [tex]-3[/tex] from right side is 1 as well. The value of [tex]f(-3)=1[/tex].
Since left hand side limit is equal to right hand side limit and it is equal to 1, therefore, [tex]\lim _{x\to -3}f\left(x\right)=1[/tex].
