Question

for the function $f(x)$ shown below, determine $lim_{x
ightarrow - 2^{+}}f(x)$. $f(x)=\begin{cases}-x^{2}+1&\text{for }x > - 2\\-5x - 6&\text{for }xleq - 2end{cases}$ answer attempt 1 out of 2

Explanation:

Step1: Identify the correct - part of the piece - wise function

We are finding $\lim_{x
ightarrow - 2^{+}}f(x)$, which means $x$ is approaching $-2$ from the right. For $x>-2$, the function is $f(x)=-x^{2}+1$.

Step2: Substitute $x = - 2$ into the relevant function

Substitute $x=-2$ into $y=-x^{2}+1$. We get $y=-(-2)^{2}+1$.
First, calculate $(-2)^{2}=4$. Then $y=-4 + 1=-3$.

Answer:

$-3$