Question

The graph of the piecewise function f(x) is shown.

Answer 1

The range is virtually the answer to the question,

"In which interval can find all y-values of the function".

So you look at the y-axis and see that your function begins with $y=-5$ (including -5 because of the dot on the graph) and ends at including $y=-1$.

So the interval notation is,

$y\in[-5,-1]$

But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,

$-5\leq y\leq-1$

To specify that this is a set use curly bracelets and a bar,

$\{y\mid-5\leq y\leq-1\}$.

The y before bar is a step function and everything followed after the vertical bar is the range of the step function.

Hope this helps.