Question

The graph of the piecewise function f(x) is shown. On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (1, 1) and goes down to an open circle at (3, negative 3). The second line has a closed circle at (3, negative 4) and continues horizontally to an open circle at (5, negative 4). What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}

Answer 1

Answer: {x | 1 < x < 5}

Step-by-step explanation:

Answer 2

Answer:

{x | 1 < x < 5}

Step-by-step explanation:

The domain of the function is the valid set to the x-variable. It's important to remember that an open circle represents the absence of that point inside the domain set.

Now, the problem describes a domain which goes from 1 to 5, because first goes from (1,1) to (3,-3), then goes from (3,-4) to (5,-4). If you observe all x-values, you will find that the domain is from x=1 to x=5, however 1 and 5 are not included because they are at an open circle. Therefore the domain is

{x | 1 < x < 5}