Question

On a coordinate plane, a piecewise function has 3 lines. The first line has an open circle at (-9, -2), continues horizontally at y = -2, then has an open circle at (0, -2). The second line has an open circle at (0, 1), continues up with a positive slope, then has an open circle at (4, 9). The third line has an open circle at (4, -2), continues down with a negative slope, then has an open circle at (8, -4).

What is the domain indicated on the graph for each portion of the piecewise function?

1st piece:
A) x ≤ -9
B) -9 < x < 0
C) x ≥ 0
D) -9 ≤ x < 0

2nd piece:
A) x ≤ 0
B) 0 < x < 4
C) x ≥ 4
D) 0 ≤ x < 4

3rd piece:
A) x ≤ 4
B) 4 < x < 8
C) x ≥ 8
D) 4 ≤ x < 8

Answer 1

The domain for each portion of the piecewise function is -9 < x < 0 for the first piece, 0 < x < 4 for the second piece, and 4 ≤ x < 8 for the third piece.

Step-by-step explanation:

The domain for each portion of the piecewise function can be determined by analyzing the open circles on the graph.

For the first line, the open circles are located at (-9, -2) and (0, -2). Since the open circles indicate that the function is not defined at those specific points, the domain for the first piece is B) -9 < x < 0.

For the second line, the open circles are located at (0, 1) and (4, 9). Again, the open circles indicate that the function is not defined at those specific points, so the domain for the second piece is B) 0 < x < 4.

For the third line, the open circles are located at (4, -2) and (8, -4). Similar to the previous cases, the function is not defined at those points, so the domain for the third piece is D) 4 ≤ x < 8.