the function f(x) is to be graphed on a coordinate plane.\nf(x)=\begin{cases}-x, & x < 0\\1, &…

the function f(x) is to be graphed on a coordinate plane.\nf(x)=\begin{cases}-x, & x < 0\\1, & xgeq0end{cases}\nat what point should an open circle be drawn?\n(-1, 0)\n(0, 0)\n(0, 1)\n(1, 0)

the function f(x) is to be graphed on a coordinate plane.\nf(x)=\begin{cases}-x, & x < 0\\1, & xgeq0end{cases}\nat what point should an open circle be drawn?\n(-1, 0)\n(0, 0)\n(0, 1)\n(1, 0)

Answer

Answer:

B. $(0,0)$

Explanation:

Step1: Understand piece - wise function

The function $f(x)$ has two parts: $f(x)=-x$ for $x < 0$ and $f(x) = 1$ for $x\geq0$.

Step2: Analyze the break - point

The break - point of the piece - wise function is at $x = 0$. For $x<0$, the function is $y=-x$. When $x = 0$ is approached from the left side ($x<0$), $y=-x$ gives $y = 0$. But the function is not defined as $y=-x$ at $x = 0$ (since the domain for $y=-x$ is $x<0$). So, an open - circle is drawn at the point $(0,0)$ which represents the non - included value of the function $y=-x$ as $x$ approaches $0$ from the left.