Question

Use the graph of the function f to determine the given limit.

Answer 1

We have been given graph of a piece-wise function. We are asked to find the limit of function as x approaches $-3$.

We can see that our given function has a jump discontinuity at $x=3$, while our function is continuous at $x=-3$.

We can see that the equation of line is $y=1$ from negative infinity to $x=3$.

The limit of f(x) as x approaches $-3$ from left side is 1 and limit of f(x) as x approaches $-3$ from right side is 1 as well. The value of $f(-3)=1$.

Since left hand side limit is equal to right hand side limit and it is equal to 1, therefore, $\lim _{x\to -3}f\left(x\right)=1$.