Question

answer the following questions about the following piece - wise function: $f(x)=\begin{cases}2x - 1 if x > - 1\\-x if xleq - 1end{cases}$ which graph matches the given function? (1 point) the closed circle occurs at the point. (1 point)

Explanation:

Step1: Analyze $x\leq - 1$ part

For $y=-x$ when $x\leq - 1$, if $x = - 1$, then $y=-(-1)=1$. The function $y = - x$ for $x\leq - 1$ is a line with slope - 1 and has a closed - circle at $x=-1$ since the inequality is $\leq$.

Step2: Analyze $x > - 1$ part

For $y = 2x-1$ when $x > - 1$, if $x=-1$, then $y=2\times(-1)-1=-3$. The function $y = 2x - 1$ for $x > - 1$ is a line with slope 2 and has an open - circle at $x=-1$ since the inequality is $>$.

Answer:

The graph where the line $y=-x$ has a closed - circle at the point $(-1,1)$ and the line $y = 2x-1$ has an open - circle at the point $(-1,-3)$ (the second graph among the options shown in the image). The closed - circle occurs at the point $(-1,1)$.