Questions: Evaluate h(-2)=h(0)=h(1)= コ． 5 コ． 4 コ 3 コ． 1 コ 0 コ 1 コ 2

Solution Steps

The domain is the set of all possible input values (x-values) for the function. The solid black circle indicates the point is included, while the open circle indicates the point is not included. The arrows indicate the function continues infinitely in the given direction.

From the graph, the first piece starts at x = -2 (included) and continues to x=1 (not included). The second piece starts at x=1 (included) and goes to the right infinitely. The third piece starts at x = -2 (included) and goes to the left infinitely.

Therefore, the domain is \\((-∞, ∞)\\) or all real numbers.

The range is the set of all possible output values (y-values) for the function.

The first piece is a horizontal line segment at y = 1 from x = -2 to just before x = 1. The second piece is a horizontal line segment at y = -4. The third piece is at y = -2 from x = -2 and toward negative infinity.

Therefore, the range is \\(\{-4, -2, 1\}\\).

A function is one-to-one if each input value (x-value) corresponds to exactly one output value (y-value), and each output value corresponds to exactly one input value. This can be checked using the horizontal line test. If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

In this case, the horizontal line at y = 1 intersects two sections of the graph (the first section from -2 to 1, and the point at x=1 in the first section), so the function is not one-to-one.

From the graph:

• \\(h(-2) = 1\\) (The solid circle at x = -2 lies on the horizontal line y=1)
• \\(h(0) = 1\\) (The graph at x = 0 lies on the horizontal line y=1)
• \\(h(1) = 1\\) (The open circle at x = 1 lies on the horizontal line y=1) The solid circle lies on the x-axis at x=1. But this takes precedence.

Final Answer