Question

The graph of the piecewise function f(x) is shown.
What is the range of f(x)?
6
5
O {x1-2 sx<4)
O {x1-2 Oy1-5 O {1-5 sys-1)
3+
2+
1
-7 -6 -5 -4 -3
-
1
3
4
5
8

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.

Answer 2

Using it's concept, it is found that the range of f(x) is given by:

{y|-5 <= -y <= -1}

What is the range of a function?

The range of a function is the set that contains all possible output values. In a graph, it is given by the values of y, that is, the values of the vertical axis.

In the function described by this graph, the vertical axis assumes values between -1 and -5, inclusive, hence the range is given by:

{y|-5 <= -y <= -1}

More can be learned about the range of a function at https://brainly.com/question/24374080