Question

(Point a) starts at 0, 3 with the arrow going straight to the right

(Point b) starts at o, -2 with the arrow going straight to the left

Choose the correct piecewise function

y = { -2x and 3x

y = { -2, x > 0 and 3, x > 0

y = { -2, x < 0 and 3, x ≥ 0

y = { -2, x > 2 and 3, x ≤ 3

Answer 1

To create a piecewise function that describes the lines defined by point \( a \) (starting at (0, 3) with an arrow going straight to the right) and point \( b \) (starting at (0, -2) with an arrow going straight to the left), we need to clarify the behavior of the lines as follows:

- From point a (0, 3) going right means that for \( x \geq 0 \), the value of \( y \) is constant at 3.
- From point b (0, -2) going left means that for \( x < 0 \), the value of \( y \) is constant at -2.

Thus, the appropriate piecewise function would be:

\[
y =
\begin{cases}
-2 & \text{if } x < 0 \\
3 & \text{if } x \geq 0
\end{cases}
\]

Among the options you provided, this is represented by the piecewise function:

**y = { -2, x < 0 and 3, x ≥ 0**