Question

graph the piecewise function $f(x)=\

$$\begin{cases}x + 5\\text{ if }x\\leq - 2\\\\2x + 3\\text{ if }x > - 2\\end{cases}$$

$. will the graph have any open endpoints? if yes, where? (1 point)\
\
\bigcirc yes, at $(-2, -1)$.\
\
\bigcirc yes, at $(-2, 3)$ and $(-2, -1)$.\
\
\bigcirc yes, at $(-2, 3)$.\
\
\bigcirc no, all endpoints are closed.

Explanation:

Step1: Evaluate first piece at x=-2

$f(-2) = (-2) + 5 = 3$
This piece includes $x \leq -2$, so $(-2, 3)$ is a closed endpoint.

Step2: Evaluate second piece at x=-2

$f(-2) = 2(-2) + 3 = -1$
This piece uses $x > -2$, so $x=-2$ is not included, making $(-2, -1)$ an open endpoint.

Step3: Identify open endpoint

Only the point from the second piece at $x=-2$ is open, since the first piece includes $x=-2$.

Answer:

Yes, at $(-2, -1)$.