Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Graph shows a piecewise function plotted on a coordinate plane. The function has two segments. One segment has a closed endpoint at (minus 3, 0) and an open endpoint at (minus 1, 2). The other segment has closed endpoints at (minus 1, 5) and (1, 5).


The graph represents the piecewise function:

Answer 1

Based on the description of the piecewise function, the function can be written as follows:

1. For the first segment (between x = -3 and x = -1, where the endpoint at -3 is closed and the endpoint at -1 is open), we can express this segment as:
\( f(x) = mx + b \) for \( -3 \leq x < -1 \)

Since we don't have the slope or y-intercept directly from the description, we cannot define it numerically. However, we know the following points:
- At \( x = -3 \), \( f(-3) = 0 \)
- At \( x = -1 \), \( f(-1) = 2 \)

2. For the second segment (between x = -1 and x = 1, where both endpoints are closed at (−1, 5) and (1, 5)), this is a constant function, so we can express this segment as:
\( f(x) = 5 \) for \( -1 \leq x \leq 1 \)

In summary, the piecewise function can be represented as:

\[
f(x) =
\begin{cases}
\text{(Linear function between (-3, 0) and (-1, 2))} & \text{if } -3 \leq x < -1 \\
5 & \text{if } -1 \leq x \leq 1
\end{cases}
\]

Replace the linear part with its specific equation if available or provide approximate numerical values if you know them from the graph.