the piece - wise function f(x) has opposite expressions.\nf(x)=\begin{cases}2x - 1, &x < 0\\0, &x = 0\\-2x +…

the piece - wise function f(x) has opposite expressions.\nf(x)=\begin{cases}2x - 1, &x < 0\\0, &x = 0\\-2x + 1, &x>0end{cases}\nwhich is the graph of f(x)?

the piece - wise function f(x) has opposite expressions.\nf(x)=\begin{cases}2x - 1, &x < 0\\0, &x = 0\\-2x + 1, &x>0end{cases}\nwhich is the graph of f(x)?

Answer

Answer:

The first graph (left - most graph)

Explanation:

Step1: Analyze (x < 0) part

For (f(x)=2x - 1) when (x < 0), the (y) - intercept is (-1) and slope is (2). When (x=-1), (y=2\times(-1)-1=-3). The line has an open - circle at (x = 0) since (x<0).

Step2: Analyze (x = 0) part

(f(0)=0), so there is a closed - circle at the point ((0,0)).

Step3: Analyze (x>0) part

For (f(x)=-2x + 1) when (x>0), the (y) - intercept is (1) and slope is (-2). When (x = 1), (y=-2\times1+1=-1). The line has an open - circle at (x = 0) since (x>0). This matches the first graph.