Question

Asking again because someone answered with something completely random when I asked it the first time. Please answer ASAP.

Answer 1

Answer: Choice C

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Step-by-step explanation:

The piecewise function is

`f(x) = \begin{cases} -3 \ \text{ if } \ -2 < x \le -1\\ -2 \ \text{ if } \ -1 < x \le 0\\ -1 \ \text{ if } \ 0 < x \le 1\\ \end{cases}`

It breaks down into these three cases

• If
  `-2 < x \le -1`, then f(x) = -3
• If
  `-1 < x \le 0`, then f(x) = -2
• If
  `0 < x \le 1`, then f(x) = -1

Only one case is possible at a time. The cases do not overlap.

So in effect, f(x) has a split personality. It changes identity based on what the x input is.

To graph this, we'll graph the pieces of the linear functions y = -3, y = -2 and y = -1. They are horizontal lines.

• We only graph y = -3 when
  `-2 < x \le -1` as described in the first piece.
• We only graph y = -2 when
  `-1 < x \le 0` based on what the second piece says.
• Lastly, we only graph y = -1 when
  `0 < x \le 1`

What results is shown in graph C. We have a step function or staircase function. The horizontal pieces of the staircase are visible, but the vertical portions are not. So the horizontal pieces are completely separate from one another. Some graphing calculators may erroneously show the vertical portions (due to how some graphing calculators have a knack for wanting to connect all the dots with one smooth curve).

Note the use of open holes vs closed circles at the endpoints of each piece. Open holes signal that the point is not part of the graph. Think of a pothole in the road that you cannot drive on. In contrast, a closed circle endpoint is part of the graph. The open holes correspond to any time we don't have "or equal to" in the inequality sign.

Answer 2

C

Step-by-step explanation:

The lines match the problem