Question

graphing a piecewise - defined function
which graph represents the piecewise - defined function $f(x)=\begin{cases}-x + 4, & 0leq x<1\\6, & xgeq1end{cases}$?

Explanation:

Step1: Analyze first - part of function

For \(f(x)= - x + 4\) where \(0\leq x<1\). When \(x = 0\), \(f(0)=-0 + 4=4\); when \(x = 1\), \(f(1)=-1 + 4 = 3\) (but \(x<1\) so this is an open - circle at \((1,3)\)). The slope of \(y=-x + 4\) is \(-1\), and it is a line segment starting at the closed - circle \((0,4)\) and going to the open - circle \((1,3)\).

Step2: Analyze second - part of function

For \(f(x)=6\) where \(x>1\). This is a horizontal line \(y = 6\) with an open - circle at \((1,6)\) and extending to the right.

Answer:

The graph that has a line segment from the closed - circle \((0,4)\) to the open - circle \((1,3)\) for \(0\leq x<1\) and a horizontal line \(y = 6\) with an open - circle at \((1,6)\) and extending to the right. (You need to visually identify this among the given options in the original problem.)