Question

unit test
unit test complete
the function f(x) is to be graphed on a coordinate plane.
$f(x)=\

$$\begin{cases}-x, & x < 0 \\\\ 1, & x \\geq 0\\end{cases}$$

$
at what point should an open circle be drawn?
$\circ$ (-1, 0)
$\circ$ (0, 0)
$\circ$ (0, 1)
$\circ$ (1, 0)
mark this and return
save and exit

Explanation:

Step1: Check the piecewise function at x=0

For \(x < 0\), \(f(x) = -x\). At \(x=0\) (not included in this part), \(f(0)\) would be \(0\).

Step2: Check the other part at x=0

For \(x \geq 0\), \(f(x) = 1\) (includes \(x=0\), so \(f(0)=1\)).

Step3: Identify the open circle point

The point \((0,0)\) is not included (since \(x < 0\) doesn't cover \(x=0\)), so it needs an open circle. The point \((0,1)\) is included (closed circle). Other options don't relate to the boundary.

Answer:

B. (0,0)