Question

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

On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).

What is the range of f(x)?

x
x
y
−5 ≤ y ≤ −1

Answer 1

The range of the given piecewise function, based on the graph provided, is the set of all y-values that the function takes. It includes closed circles at both -5 and -1, so the range is y .

Step-by-step explanation:

The student is asked to determine the range of a piecewise function based on its graphical representation. To find the range, we focus on the y-values that the function takes on the graph. The graph has two parts: a line from the point (-2, -5) with a closed circle (indicating that -5 is included in the range) to the point (2, -1) with a closed circle (indicating -1 is also included), and a second line from (2, -1) with a closed circle to (4, -2) with an open circle (indicating that -2 is not included in the range).

Since the first line segment includes points on the graph within the y-values from -5 up to -1, and the second line segment continues at y = -1 and moves downwards but stops just before reaching -2 (due to the open circle at (4, -2)), the entire range of the function is from -5 to -1, inclusive. Therefore, the range of the function is -5 ≤ y ≤ -1, which corresponds to the fourth option provided.