Question

function analysis online practice part 1
complete this assessment to review what youve learned. it will not count toward your grade.
which point should have an open circle in the graph of the piece - wise function $f(x)=\begin{cases}-x - 1&\text{if }x<1\\-x + 2&\text{if }xgeq1end{cases}$? (1 point)
(1,1)
(-1,1)
(-1,-2)
(1,-2)
check answer
remaining attempts 3

Explanation:

Step1: Analyze the domain of the piece - wise function

The function $f(x)$ changes its rule at $x = 1$. The first part $y=-x - 1$ is for $x<1$ and the second part $y=-x + 2$ is for $x\geq1$. An open - circle is used for values of $x$ that are not included in the domain of a particular part of the piece - wise function.

Step2: Evaluate the first part of the function at $x = 1$

For $y=-x - 1$ when $x = 1$, we substitute $x = 1$ into $y=-x - 1$. So $y=-1-1=-2$. Since $x = 1$ is not in the domain $x<1$ for this part of the function, the point $(1,-2)$ will have an open - circle on the graph.

Answer:

$(1,-2)$