Question

Which of the following gives the correct range for the piecewise graph? A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4. −4 ≤ x ≤ 2 −3 ≤ x ≤ 5 −4 ≤ y ≤ 2 −3 ≤ y ≤ 5

Answer 1

Answer: -4 ≤ y ≤ 2

Explanation:

The correct range for the piecewise graph given in the question is -4 ≤ y ≤ 2.

To find the range, we need to look at the y-coordinates of the points on the graph.

The y-coordinate of the point (-3, 2) is 2 and the y-coordinate of the point (0, 1) is also 1.

Therefore, the range for the first segment is 2 ≤ y ≤ 1.

Similarly, the y-coordinate of the point (0, 1) is 1 and the y-coordinate of the point (5, -4) is -4.

Therefore, the range for the second segment is 1 ≤ y ≤ -4.

So, the overall range for the entire graph is the intersection of these two ranges, which is -4 ≤ y ≤ 1.

Hence, the correct range for the piecewise graph is -4 ≤ y ≤ 2.

Therefore, the correct option is -4 ≤ y ≤ 2.