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`.